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1
Blackburn, Simon R. "Group enumeration." Thesis, University of Oxford, 1992. http://ora.ox.ac.uk/objects/uuid:caac5ed0-44e3-4bec-a97e-59e11ea268af.
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The thesis centres around two problems in the enumeration of p-groups. Define f<sub>φ</sub>(p<sup>m</sup>) to be the number of (isomorphism classes of) groups of order p<sup>m</sup> in an isoclinism class φ. We give bounds for this function as φ is fixed and m varies and as m is fixed and φ varies. In the course of obtaining these bounds, we prove the following result. We say a group is reduced if it has no non-trivial abelian direct factors. Then the rank of the centre Z(P) and the rank of the derived factor group P|P' of a reduced p-group P are bounded in terms of the orders of P|Z(P)P' and P'∩Z(P). A long standing conjecture of Charles C. Sims states that the number of groups of order p<sup>m</sup> is<br/> p<sup><sup>2</sup>andfrasl;<sub>27</sub>m<sup>3</sup>+O(m<sup>2</sup>)</sup>. (1) We show that the number of groups of nilpotency class at most 3 and order p<sup>m</sup> satisfies (1). We prove a similar result concerning the number of graded Lie rings of order p<sup>m</sup> generated by their first grading.
2
Mishna, Marni. "Cayley graph enumeration." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ51422.pdf.
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Shoilekova, Bilyana Todorova. "Graphical enumeration methods." Thesis, University of Oxford, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.526538.
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Hannah, Stuart A. "Interval order enumeration." Thesis, University of Strathclyde, 2015. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=26137.
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This thesis continues the study of interval orders and related structures, containing results on both the labeled and unlabeled variants. Following a result of Eriksen and Sjöstrand (2014) we identify a link between structures following the Fishburn distribution and Mahonian structures. This is used to detail a technique for the construction of Fishburn structures (structures in bijection with unlabeled interval orders) from appropriate Mahonian structures. This technique is introduced on a bivincular pattern of Bousquet-Mélou et al. (2010) and then used to introduce a previously unconsidered class of matchings; explicitly, zero alignment matchings according to the number of arcs which are both right-crossed and left-nesting. The technique is then used to identify a statistic on the factorial posets of Claesson and Linusson (2011) following the Fishburn distribution. Factorial posets mapped to zero by this statistic are canonically labeled factorial posets which may alternatively be viewed as unlabeled interval orders. As a consequence of our approach we find an identity for the Fishburn numbers in terms of the Mahonian numbers and discuss linear combinations of Fishburn patterns in a manner similar to that of the Mahonian combinations of Babson and Steingrímsson (2001). To study labeled interval orders we introduce ballot matrices, a signed combinatorial structure whose definition naturally follows from the generating function for labeled interval orders. A sign reversing involution on ballot matrices is defined. Adapting a bijection of Dukes, Jelínek and Kibitzke (2011), we show that matrices fixed under this involution are in bijection with labeled interval orders and that they decompose to a pair consisting of a permutation and an inversion table. To fully classify such pairs results pertaining to the enumeration of permutations having a given set of ascent bottoms are given. This allows for a new formula for the number of labeled interval orders.
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Edeson, Margaret, and n/a. "Investigations in coset enumeration." University of Canberra. Information Sciences & Engineering, 1989. http://erl.canberra.edu.au./public/adt-AUC20050712.083514.
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The process of coset enumeration has become a significant factor in
group theoretical investigations since the advent of modern computing
power, but in some respects the process is still not well understood.
This thesis investigates some features of coset enumeration, working
mainly with the group F(2,7).
Chapter 1 describes the characteristics of coset enumeration and
algorithms used for it. A worked example of the method is provided.
Chapter 2 discusses some features which would be desirable in computer
programs for use in investigating the coset enumeration process itself,
and reviews the Havas/Alford program which to date best meets the
requirements.
Chapter 3 deals with the use of coset ammeration in proofs, either in
its own right or as a basis for other workings. An example of one
attempt to obtain a proof by coset enumeration is given.
Chapter 4 reviews techniques designed to reduce the length of coset
enumerations and proposes the 'equality list' technique as a way to
reduce enumeration length for some groups. Extra insights obtainable
using the equality list method are also discussed.
Chapter 5 summarises the factors by which the success of different
coset enumerations can be compared and proposes an algorithm for making
systematic comparisons among enumerations.
Chapter 6 reports five coset enumerations, obtained manually by three
main methods on the group F(2,7). All these enumerations were shorter
than is so far obtainable by machine and one is shorter than other
known hand enumerations. The enumerations were compared by applying
the process developed in Chapter 5.
Chapter 7 presents a shorter proof of the cyclicity of the group F(2,7)
than was hitherto available. The proof derives from the workings for
one of the coset enumerations described in Chapter 6.
There are eight appendices and an annotated bibliography. The
appendices contain, inter alia, edited correspondence between
well-known coset-enumerators, a guide to the Havas/Alford program,
further details on the equality list method and listings of various
enumerations.
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Ocansey, Evans Doe. "Enumeration problems on lattices." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/80393.
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Thesis (MSc)--Stellenbosch University, 2013.<br>ENGLISH ABSTRACT: The main objective of our study is enumerating spanning trees (G) and perfect matchings
PM(G) on graphs G and lattices L. We demonstrate two methods of enumerating
spanning trees of any connected graph, namely the matrix-tree theorem and as a special
value of the Tutte polynomial T(G; x; y).
We present a general method for counting spanning trees on lattices in d 2 dimensions.
In particular we apply this method on the following regular lattices with d = 2:
rectangular, triangular, honeycomb, kagomé, diced, 9 3 lattice and its dual lattice to
derive a explicit formulas for the number of spanning trees of these lattices of finite sizes.
Regarding the problem of enumerating of perfect matchings, we prove Cayley’s theorem
which relates the Pfaffian of a skew symmetric matrix to its determinant. Using
this and defining the Pfaffian orientation on a planar graph, we derive explicit formula for
the number of perfect matchings on the following planar lattices; rectangular, honeycomb
and triangular.
For each of these lattices, we also determine the bulk limit or thermodynamic limit,
which is a natural measure of the rate of growth of the number of spanning trees (L)
and the number of perfect matchings PM(L).
An algorithm is implemented in the computer algebra system SAGE to count the
number of spanning trees as well as the number of perfect matchings of the lattices
studied.<br>AFRIKAANSE OPSOMMING: Die hoofdoel van ons studie is die aftelling van spanbome (G) en volkome afparings
PM(G) in grafieke G en roosters L. Ons beskou twee metodes om spanbome in ’n samehangende
grafiek af te tel, naamlik deur middel van die matriks-boom-stelling, en as ’n
spesiale waarde van die Tutte polinoom T(G; x; y).
Ons behandel ’n algemene metode om spanbome in roosters in d 2 dimensies af te
tel. In die besonder pas ons hierdie metode toe op die volgende reguliere roosters met
d = 2: reghoekig, driehoekig, heuningkoek, kagomé, blokkies, 9 3 rooster en sy duale
rooster. Ons bepaal eksplisiete formules vir die aantal spanbome in hierdie roosters van
eindige grootte.
Wat die aftelling van volkome afparings aanbetref, gee ons ’n bewys van Cayley se
stelling wat die Pfaffiaan van ’n skeefsimmetriese matriks met sy determinant verbind.
Met behulp van hierdie stelling en Pfaffiaanse oriënterings van planare grafieke bepaal
ons eksplisiete formules vir die aantal volkome afparings in die volgende planare roosters:
reghoekig, driehoekig, heuningkoek.
Vir elk van hierdie roosters word ook die “grootmaat limiet” (of termodinamiese limiet)
bepaal, wat ’n natuurlike maat vir die groeitempo van die aantaal spanbome (L) en die
aantal volkome afparings PM(L) voorstel.
’n Algoritme is in die rekenaaralgebra-stelsel SAGE geimplementeer om die aantal
spanboome asook die aantal volkome afparings in die toepaslike roosters af te tel.
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Meier, Arne [Verfasser]. "Parametrised enumeration / Arne Meier." Hannover : Gottfried Wilhelm Leibniz Universität Hannover, 2020. http://d-nb.info/1206685859/34.
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Ramos, Garrido Lander. "Graph enumeration and random graphs." Doctoral thesis, Universitat Politècnica de Catalunya, 2017. http://hdl.handle.net/10803/405943.
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In this thesis we use analytic combinatorics to deal with two related problems: graph enumeration and random graphs from constrained classes of graphs. We are interested in drawing a general picture of some graph families by determining, first, how many elements are there of a given possible size (graph enumeration), and secondly, what is the typical behaviour of an element of fixed size chosen uniformly at random, when the size tends to infinity (random graphs). The problems concern graphs subject to global conditions, such as being planar and/or with restrictions on the degrees of the vertices.
In Chapter 2 we analyse random planar graphs with minimum degree two and three. Using techniques from analytic combinatorics and the concepts of core and kernel of a graph, we obtain precise asymptotic estimates and analyse relevant parameters for random graphs, such as the number of edges or the size of the core, where we obtain Gaussian limit laws. More challenging is the extremal parameter equal to the size of the largest tree attached to the core. In this case we obtain a logarithmic estimate for the expected value together with a concentration result.
In Chapter 3 we study the number of subgraphs isomorphic to a fixed graph in subcritical classes of graphs. We obtain Gaussian limit laws with linear expectation and variance when the fixed graph is 2-connected. The main tool is the analysis of infinite systems of equations by Drmota, Gittenberger and Morgenbesser, using the theory of compact operators. Computing the exact constants for the first estimates of the moments is in general out of reach. For the class of series-parallel graphs we are able to compute them in some particular interesting cases.
In Chapter 4 we enumerate (arbitrary) graphs where the degree of every vertex belongs to a fixed subset of the natural numbers. In this case the associated generating functions are divergent and our analysis uses instead the so-called configuration model. We obtain precise asymptotic estimates for the number of graphs with given number of vertices and edges and subject to the degree restriction. Our results generalize widely previous special cases, such as d-regular graphs or graphs with minimum degree at least d.<br>En aquesta tesi utilitzem l'analítica combinatòria per treballar amb dos problemes relacionats: enumeració de grafs i grafs aleatoris de classes de grafs amb restriccions. En particular ens interessa esbossar un dibuix general de determinades famílies de grafs determinant, en primer lloc, quants grafs hi ha de cada mida possible (enumeració de grafs), i, en segon lloc, quin és el comportament típic d'un element de mida fixa triat a l'atzar uniformement, quan aquesta mida tendeix a infinit (grafs aleatoris). Els problemes en què treballem tracten amb grafs que satisfan condicions globals, com ara ésser planars, o bé tenir restriccions en el grau dels vèrtexs. En el Capítol 2 analitzem grafs planar aleatoris amb grau mínim dos i tres. Mitjançant tècniques de combinatòria analítica i els conceptes de nucli i kernel d'un graf, obtenim estimacions asimptòtiques precises i analitzem paràmetres rellevants de grafs aleatoris, com ara el nombre d'arestes o la mida del nucli, on obtenim lleis límit gaussianes. També treballem amb un paràmetre que suposa un repte més important: el paràmetre extremal que es correspon amb la mida de l'arbre més gran que penja del nucli. En aquest cas obtenim una estimació logarítmica per al seu valor esperat, juntament amb un resultat sobre la seva concentració. En el Capítol 3 estudiem el nombre de subgrafs isomorfs a un graf fix en classes de grafs subcrítiques. Quan el graf fix és biconnex, obtenim lleis límit gaussianes amb esperança i variància lineals. L'eina principal és l'anàlisi de sistemes infinits d'equacions donada per Drmota, Gittenberger i Morgenbesser, que utilitza la teoria d'operadors compactes. El càlcul de les constants exactes de la primera estimació dels moments en general es troba fora del nostre abast. Per a la classe de grafs sèrie-paral·lels podem calcular les constants en alguns casos particulars interessants. En el Capítol 4 enumerem grafs (arbitraris) el grau de cada vèrtex dels quals pertany a un subconjunt fix dels nombres naturals. En aquest cas les funcions generatrius associades són divergents i la nostra anàlisi utilitza l'anomenat model de configuració. El nostre resultat consisteix a obtenir estimacions asimptòtiques precises per al nombre de grafs amb un nombre de vèrtexs i arestes donat, amb la restricció dels graus. Aquest resultat generalitza àmpliament casos particulars existents, com ara grafs d-regulars, o grafs amb grau mínim com a mínim d.
9
Postnikov, Alexander. "Enumeration in algebra and geometry." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/42693.
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Egebrand, August. "Feynman Diagrams and Map Enumeration." Thesis, Uppsala universitet, Teoretisk fysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-298474.
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The goal of this thesis is to count how many graphs exist given a number of verticesor some other restrictions. The graphs are counted by perturbing Gaussian integralsand using the Wick lemma to interpret the perturbations in terms of graphs. Fatgraphs, a specific type of graph, are central in this thesis. A method based onorthogonal polynomials to count fat graphs is presented. The thesis finishes with theformulation and some results related to the three-color problem.
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Strozecki, Yann. "Enumeration complexity and matroid decomposition." Paris 7, 2010. http://www.theses.fr/2010PA077178.
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Ce travail comporte deux parties principales, d'une part l'étude des algorithmes d'énumération et leur complexité et d'autres part la vérification pour des hypergraphes et des matroïdes décomposés de propriétés exprimés en logique monadique du second ordre. L'énumération est d'abord étudié d'un point de vue structurel : on donne les définitions des classes de complexité les plus naturelles et leur relations sont étudiées. On tente d'expliquer le rôle de l'ordre dans cette problématique ainsi que l'effet d'opérations ensemblistes sur les solutions. Puis on donne une série de résultats sur l'énumération des monômes de polynômes donnés soit comme des boîtes noires, soit comme des circuits. Les algorithmes développés peuvent ensuite être utilisés pour résoudre des problèmes combinatoires plus classiques, tel que l'énumération des hyperarbres couvrants d'un hypergraphe 3-uniforme. Dans la deuxième partie, on donne une représentation arborescente alternative des matroïdes de largeur de branche bornée. Cela permet d'exprimer localement la propriété d'indépendance et ainsi de décider en temps linéaire des propriétés monadiques du second ordre sur ces structures. On obtient également une énumération à délai linéaire des objets définissables en LMSO, par exemple les circuits d'un matroïde. On montre que cette décomposition s'étend facilement à d'autres classes de matroïdes et en poussant l'abstraction plus loin à des hypergraphes décomposables<br>This thesis is made of two parts, on the one hand the study of enumeration algorithms and their complexity and in the other hand the model checking of Monadic second order properties over decomposable matroids. The enumeration is studied first from a structural point of view: natural complexity classes are defined and their relation studied. We also try to explain the effect of ordering in enumeration and of some set operations over the solutions. Then, we present several algorithms to enumerate the monomials of polynomials given either as black boxes or circuits. They can be used to solve more classical combinatoric problems such as the enumeration of spanning hypertrees of a 3-uniform hypergraph. In the second part, we present an alternative tree decomposition of representable matroids of bounded branch-width. It enables to locally express the dependency property and thus to give a linear time algorithm to check MSO properties over these structures. We also obtain a linear delay enumeration algorithm of the objects definable in MSO, such as the circuits of a matroid. This decomposition can easily extended to other classes and even by further abstraction to hypergaphs
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Lladser, Manuel Eugenio. "Asymptotic enumeration via singularity analysis." Connect to this title online, 2003. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1060976912.
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Thesis (Ph. D.)--Ohio State University, 2003.<br>Title from first page of PDF file. Document formatted into pages; contains x, 227 p.; also includes graphics Includes bibliographical references (p. 224-227). Available online via OhioLINK's ETD Center
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Badillo, Sanchez Liliana. "Genericity in the enumeration degrees." Thesis, University of Leeds, 2013. http://etheses.whiterose.ac.uk/5296/.
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In this thesis we study the notion of enumeration 1-genericity, various basic properties of it and its relationship with 1-genericity. We also study the problem of avoiding uniformity in the �02 enumeration degrees. In Chapter 2 we give a brief background survey of the notion of genericity in the context of the Turing degrees as well as in the enumeration degrees. Chapter 3 presents a brief overview of the relationship between noncupping and genericity in the enumeration degrees. We give a result that will be useful in proving the existence of prime ideals of �02 enumeration degrees in Chapter 5, namely, we show the existence of a 1-generic enumeration degree 0e < a < 00 e which is noncuppable and low2. In Chapter 4 we investigate the property of incomparability relative to a class of degrees of a speci�c level of the Arithmetical Hierarchy. We show that for every uniform �02 class of enumeration degrees C, there exists a high �02 enumeration degree c which is incomparable with any degree b 2 C such that b =2 f0e; 00 e g. Chapter 5 is devoted to the introduction of the notions of \enumeration 1- genericity" and \symmetric enumeration 1-genericity". We study the distribution of the enumeration 1-generic degrees and show that it resembles to some extent the distribution of the class of 1-generic degrees. We also present an application of enumeration 1-genericity to show the existence of prime ideals of �02 enumeration degrees. We then look at the relationship between enumeration 1-genericity and highness. Finally, in Chapter 6 we present two di�erent approaches to the problem of separating the class of the enumeration 1-generic degrees from the class of 1-generic degrees. One of them is by showing the existence of a non trivial enumeration 1- generic set which is not 1-generic and the other is by proving that there exists a property that both classes do not share, namely, nonsplitting.
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Markwig, Hannah. "The enumeration of plane tropical curves." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980700736.
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Distler, Andreas. "Classification and enumeration of finite semigroups." Thesis, St Andrews, 2010. http://hdl.handle.net/10023/945.
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Wong, Thomas. "Enumeration problems in directed walk models." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/54483.
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Self-avoiding walks appear ubiquitously in the study of linear polymers as it naturally captures their volume exclusion property. However, self-avoiding walks are very difficult to analyse with few rigourous results available. In 2008, Alvarez et al. determined numerical results for the forces induced by a self-avoiding walk in an interactive slit. These results resembled the exact results for a directed model in the same setting by Brak et al., suggesting the physical consistency of directed walks as polymer models. In the directed walk model, three phases were identified in the infinite slit limit as well as the regions of attractive and repulsive forces induced by the polymer on the walls. Via the kernel method, we extend the model to include two directed walks as a way to find exact enumerative results for studying the behaviour of ring polymers near an interactive wall, or walls. We first consider a ring polymer near an interactive surface via two friendly walks that begin and end together along a single wall. We find an exact solution and provide a full analysis of the phase diagram, which admits three phase transitions. The model is extended to include a second wall so that two friendly walks are confined in an interactive slit. We find and analyse the exact solution of two friendly walks tethered to different walls where single interactions are permitted. That is, each walk interacts with the wall it is tethered to. This model exhibits repulsive force only in the parameter space. While these results differ from the single polymer models, they are consistent with Alvarez et al.
Finally, we consider the model with double interactions, where each walk interacts with both walls. We are unable to find exact solutions via the kernel method. Instead, we use transfer matrices to obtain numerical results to identify regions of attractive and repulsive forces. The results we obtain are qualitatively similar to those presented in Alvarez et al. Furthermore, we provide evidence that the zero force curve does not satisfy any simple polynomial equation.<br>Science, Faculty of<br>Mathematics, Department of<br>Graduate
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Williams, Elizabeth C. "A study of Polya's enumeration theorem." Auburn, Ala., 2005. http://repo.lib.auburn.edu/2005%20Summer/master's/WILLIAMS_ELIZABETH_6.pdf.
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Horton, Leslie Biggs Morrison. "Enumeration of independent sets in graphs /." Full text available from ProQuest UM Digital Dissertations, 2007. http://0-proquest.umi.com.umiss.lib.olemiss.edu/pqdweb?index=2&did=1414120471&SrchMode=1&sid=1&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1219778252&clientId=22256.
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Wong, Thomas. "Enumeration problems in Baumslag-Solitar groups." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/29028.
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Geometric group theory refers to the study of finitely generated groups and their properties by exploring the algebraic and topological structure. This thesis will look at various enumeration problems that arises in Baumslag-Solitar groups. Initially, this thesis aims to reproduce and validate some of the work that has been done on the questions of growth, cogrowth and geodesic elements via an enumeration approach. This approach will then be used to explore specific examples of Baumslag-Solitar groups where these questions have not been fully answered.
The first part of this thesis will look at the growth of a horocyclic subgroup in Baumslag-Solitar groups. It will then build upon this to develop an algorithm to count the elements of the group in general out to a fixed radius with the intention of further understanding the unresolved cases.
The second part of this thesis will use Baumslag-Solitar groups as a basis to develop numerical tests to estimate cogrowth of groups. Since the cogrowth of a group is directly related to the amenability of the group, these numerical tests for cogrowth can be applied to groups such that Thompson's group F, where the question of amenability is still highly debated.
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Edwards, K. "Topics in computational complexity and enumeration." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376892.
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Harris, Charles Milton. "Enumeration reducibility and polynomial time bounds." Thesis, University of Leeds, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.426857.
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An, Junkyu. "Combinatorial enumeration of weighted Catalan numbers." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/64609.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 69-70).<br>This thesis is devoted to the divisibility property of weighted Catalan and Motzkin numbers and its applications. In Chapter 1, the definitions and properties of weighted Catalan and Motzkin numbers are introduced. Chapter 2 studies Wilf conjecture on the complementary Bell number, the alternating sum of the Stirling number of the second kind. Congruence properties of the complementary Bell numbers are found by weighted Motkin paths, and Wilf conjecture is partially proved. In Chapter 3, Konvalinka conjecture is proved. It is a conjecture on the largest power of two dividing weighted Catalan number, when the weight function is a polynomial. As a corollary, we provide another proof of Postnikov and Sagan of weighted Catalan numbers, and we also generalize Konvalinka conjecture for a general weight function.<br>by Junkyu An.<br>Ph.D.
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Ramachandran, J. "Enumeration and advice in structural complexity /." The Ohio State University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487862399450835.
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Vigny, Alexandre. "Query enumeration and nowhere dense graphs." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC211.
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Les travaux présentés dans ma thèse se situent à l’interface entre complexité, algorithmique et logique. Plus particulièrement, on s’intéresse à la complexité d'évaluation de requêtes.Plus précisément, étant donné G un graphe fini. Une requête q définit un sous ensemble de k-uplets de sommets de G que l'on note q(G). On appelle k l'arité de q et on se essaye alors d'effectuer efficacement les taches suivantes :1) décider si l'ensemble q(G) est vide ou non.2) décider si un k-uplet donné appartient à l'ensemble des solutions q(G).3) calculer le nombre de solutions.4) énumérer les éléments de q(G).En ce qui concerne la 4ème tache, un algorithme qui va énumérer les solutions sera décomposé en deux parties. La première est appelé le pré-calcul et sert à préparer l’énumération. Idéalement cette étape de requière qu’un temps linéaire en la taille du graphe. La deuxième étape est ensuite l’énumération des solutions. Le temps nécessaire pour obtenir une nouvelle solution est appelé le délai. Idéalement on souhaite que le délai de dépende pas de la taille du graphes mais uniquement de la taille de la requête. On parle alors d’énumération à délai constant après pré-calcul linéaire.Au début de cette thèse, une grand part des interrogations au sujet des classes de graphes pour lesquelles une énumération à délai constant serait possible semblait se trouver au niveau des classes de graphes nulle-part dense. Le résultat principal de cette thèse est de montrer qu’il est possible d’énumérer les solutions des requêtes du premier ordre sur les graphes nulle-part dense avec un délai constant après un pré-calcul pseudo linéaire<br>The topic of my thesis lies between complexity, algorithmic and logic. In particular, we are interested in the complexity of evaluating query.More precisely, given G a finite graph. A query q defines a subset of k-tuples of vertices of G that we note q(G). We call k the arity of q and we then try to efficiently perform the following tasks:1) decide whether the set q G) is empty.2) decide whether a given k-tuplet belongs to the set of solutions q(G).3) calculate the number of solutions.4) enumerate the elements of q(G).Regarding the 4th task, an algorithm that will enumerate the solutions can be decomposed into two steps. The first is called preprocessing and is used to prepare the enumeration. Ideally this step only requires a time linear in the size of the graph. The second step is the enumeration properly speaking. The time needed to get a new solution is called the delay. Ideally we want the delay to not depend on the size of the graph but only on the size of the query. We then talk about constant delay enumeration after linear preprocessing.At the beginning of this thesis, a large part of the interrogations about classes of graphs for which a constant delay enumeration is possible seemed to be located around the classes of nowhere dense graphs
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Little, David P. "Q-enumeration of classical combinatorial structures /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2000. http://wwwlib.umi.com/cr/ucsd/fullcit?p9989758.
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Richardson, Steven L. "Enumeration of the generalized Catalan numbers." Morgantown, W. Va. : [West Virginia University Libraries], 2005. https://etd.wvu.edu/etd/controller.jsp?moduleName=documentdata&jsp%5FetdId=3906.
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Seager, Charles. "Symmetric Presentations and Double Coset Enumeration." CSUSB ScholarWorks, 2018. https://scholarworks.lib.csusb.edu/etd/783.
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In this project, we demonstrate our discovery of original symmetric presentations and constructions of important groups, including nonabelian simple groups, and groups that have these as factor groups. The target nonabelian simple groups include alternating, linear, and sporadic groups. We give isomorphism types for each finite homomorphic image that has been found. We present original symmetric presentations of $M_{12}$, $M_{21}:(2 \times 2)$, $L_{3}(4):2^2$, $2:^{\cdot}L_{3}(4):2$, $S(4,3)$, and $S_{7}$ as homomorphism images of the progenitors $2^{*20}$ $:$ $A_{5}$, $2^{*10}$ $:$ $PGL(2,9)$, $2^{*10}$ $:$ $Aut(A_{6})$, $2^{*10}$ $:$ $A_{6}$, $2^{*10}$ $:$ $A_{5}$, and $2^{*24}$ $:$ $S_{5}$, respectively. We also construct $M_{12}$, $M_{21}:(2 \times 2)$, $L_{3}(4):2^2$, $L_{3}(4):2^2$, $2:^{\cdot}L_{3}(4):2$, $S(4,3)$, and $S_{7}$ over $A_{5}$, $PGL(2,9)$, $Aut(A_{6})$, $A_{6}$, $A_{5}$, and $S_{5}$, respectively, using our technique of double coset enumeration. All of the symmetric presentations given are original to the best of our knowledge.
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Baudin, Alexis. "Cliques statiques et temporelles : algorithmes d'énumération et de détection de communautés." Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS609.
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Les graphes sont des objets mathématiques qui permettent de modéliser des interactions ou connexions entre entités de types variés. Un graphe peut représenter par exemple un réseau social qui connecte les utilisateurs entre eux, un réseau de transport comme le métro où les stations sont connectées entre elles, ou encore un cerveau avec les milliards de neurones en interaction qu'il contient. Depuis quelques années, la forte dynamicité de ces structures a été mise en évidence, ainsi que l'importance de prendre en compte l'évolution temporelle de ces réseaux pour en comprendre le fonctionnement. Alors que de nombreux concepts et algorithmes ont été développés sur les graphes pour décrire des structures de réseaux statiques, il reste encore beaucoup à faire pour formaliser et développer des algorithmes pertinents pour décrire la dynamique des réseaux réels. Cette thèse vise à mieux comprendre comment sont structurés les graphes massifs qui sont issus du monde réel et à développer des outils pour étendre notre compréhension à des structures évoluant dans le temps. Il a été montré que ces graphes ont des propriétés particulières, qui les distinguent des graphes théoriques ou tirés aléatoirement. Exploiter ces propriétés permet alors de concevoir des algorithmes pour résoudre certains problèmes difficiles beaucoup plus rapidement sur ces instances que dans le cas général. La thèse se focalise sur les cliques, qui sont des groupes d'éléments tous connectés entre eux. Nous étudions l'énumération des cliques dans les graphes statiques et temporels et la détection de communautés qu'elles permettent de mettre en œuvre. Les communautés d'un graphe sont des ensembles de sommets tels qu'au sein d'une communauté, les sommets interagissent fortement entre eux, et peu avec le reste du graphe. Leur étude aide à comprendre les propriétés structurelles et fonctionnelles des réseaux. Nous évaluons nos algorithmes sur des graphes massifs issus du monde réel, ouvrant ainsi de nouvelles perspectives pour comprendre les interactions au sein de ces réseaux. Nous travaillons d'abord sur des graphes, sans tenir compte de la composante temporelle des interactions. Nous commençons par utiliser la méthode de détection de communautés par percolation de cliques, en mettant en évidence ses limites en mémoire, qui empêchent de l'appliquer à des graphes trop massifs. En introduisant un algorithme de résolution approchée du problème, nous dépassons cette limite. Puis, nous améliorons l'énumération des cliques maximales dans le cas des graphes particuliers dits bipartis. Ils correspondent à des interactions entre des groupes de sommets de type différent, par exemple des liens entre des personnes et du contenu consulté, la participation à des événements, etc. Ensuite, nous considérons des interactions qui ont lieu au cours du temps, grâce au formalisme des flots de liens. Nous cherchons à étendre les algorithmes présentés en première partie, pour exploiter leurs avantages dans l'étude des interactions temporelles. Nous fournissons un nouvel algorithme d'énumération des cliques maximales dans les flots de liens, beaucoup plus efficace que l'état de l'art sur des jeux de données massifs. Enfin, nous nous intéressons aux communautés dans les flots de liens par percolation de cliques, en développant une extension de la méthode utilisée sur les graphes. Les résultats montrent une amélioration significative par rapport à l'état de l'art, et nous analysons les communautés obtenues pour fournir des informations pertinentes sur l'organisation des interactions temporelles dans les flots de liens. Mon travail de thèse a permis d’apporter de nouvelles réflexions sur l’étude des réseaux massifs issus du monde réel. Cela montre l'importance d'explorer le potentiel des graphes dans un contexte réel, et pourrait contribuer à l'émergence de solutions novatrices pour les défis complexes de notre société moderne<br>Graphs are mathematical objects used to model interactions or connections between entities of various types. A graph can represent, for example, a social network that connects users to each other, a transport network like the metro where stations are connected to each other, or a brain with the billions of interacting neurons it contains. In recent years, the dynamic nature of these structures has been highlighted, as well as the importance of taking into account the temporal evolution of these networks to understand their functioning. While many concepts and algorithms have been developed on graphs to describe static network structures, much remains to be done to formalize and develop relevant algorithms to describe the dynamics of real networks. This thesis aims to better understand how massive graphs are structured in the real world, and to develop tools to extend our understanding to structures that evolve over time. It has been shown that these graphs have particular properties, which distinguish them from theoretical or randomly drawn graphs. Exploiting these properties then enables the design of algorithms to solve certain difficult problems much more quickly on these instances than in the general case. My PhD thesis focuses on cliques, which are groups of elements that are all connected to each other. We study the enumeration of cliques in static and temporal graphs and the detection of communities they enable. The communities of a graph are sets of vertices such that, within a community, the vertices interact strongly with each other, and little with the rest of the graph. Their study helps to understand the structural and functional properties of networks. We are evaluating our algorithms on massive real-world graphs, opening up new perspectives for understanding interactions within these networks. We first work on graphs, without taking into account the temporal component of interactions. We begin by using the clique percolation method of community detection, highlighting its limitations in memory, which prevent it from being applied to graphs that are too massive. By introducing an approximate problem-solving algorithm, we overcome this limitation. Next, we improve the enumeration of maximal cliques in the case of bipartite graphs. These correspond to interactions between groups of vertices of different types, e.g. links between people and viewed content, participation in events, etc. Next, we consider interactions that take place over time, using the link stream formalism. We seek to extend the algorithms presented in the first part, to exploit their advantages in the study of temporal interactions. We provide a new algorithm for enumerating maximal cliques in link streams, which is much more efficient than the state-of-the-art on massive datasets. Finally, we focus on communities in link streams by clique percolation, developing an extension of the method used on graphs. The results show a significant improvement over the state of the art, and we analyze the communities obtained to provide relevant information on the organization of temporal interactions in link streams. My PhD work has provided new insights into the study of massive real-world networks. This shows the importance of exploring the potential of graphs in a real-world context, and could contribute to the emergence of innovative solutions for the complex challenges of our modern society
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Cook, David II. "LEFSCHETZ PROPERTIES AND ENUMERATIONS." UKnowledge, 2012. http://uknowledge.uky.edu/math_etds/3.
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An artinian standard graded algebra has the weak Lefschetz property if the multiplication by a general linear form induces maps of maximal rank between consecutive degree components. It has the strong Lefschetz property if the multiplication by powers of a general linear form also induce maps of maximal rank between the appropriate degree components. These properties are mainly studied for the constraints they place, when present, on the Hilbert series of the algebra. While the majority of research on the Lefschetz properties has focused on characteristic zero, we primarily consider the presence of the properties in positive characteristic. We study the Lefschetz properties by considering the prime divisors of determinants of critical maps.
First, we consider monomial complete intersections in a finite number of variables. We provide two complements to a result of Stanley. We next consider monomial almost complete intersections in three variables. We connect the characteristics in which the weak Lefschetz property fails with the prime divisors of the signed enumeration of lozenge tilings of a punctured hexagon. Last, we study how perturbations of a family of monomial algebras can change or preserve the presence of the Lefschetz properties. In particular, we introduce a new strategy for perturbations rooted in techniques from algebraic geometry.
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Pardo, David Wilson de Abreu. "Direitos fundamentais não enumerados." Florianópolis, SC, 2005. http://repositorio.ufsc.br/handle/123456789/102251.
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Tese (doutorado) - Universidade Federal de Santa Catarina, Centro de Ciências Jurídicas. Programa de Pós-Graduação em Direito.<br>Made available in DSpace on 2013-07-16T00:26:39Z (GMT). No. of bitstreams: 1
223094.pdf: 1524627 bytes, checksum: 418e3fbacdb65fd1f862aedc0012c187 (MD5)<br>A presente tese tem por objetivo elaborar um estudo sobre o reconhecimento de novos direitos fundamentais, mais além daqueles expressamente enumerados no catálogo formal de uma constituição. A tese é dividida em cinco capítulos, contendo ainda as obrigatórias introdução e conclusão. O capítulo inicial trata de rever a idéia de constituição material, para o fim de apresentar uma noção plausível de direitos fundamentais em sentido material e, em conseqüência, de direitos fundamentais não enumerados. No segundo capítulo, demonstra-se que o reconhecimento de novos direitos fundamentais é uma questão de interpretação e aplicação da constituição. Nesse sentido, direitos fundamentais não enumerados constituem uma questão interpretativa. O capítulo terceiro é reservado para o exame da justificação dos direitos fundamentais na teoria do discurso, defendendo a natureza moral do empreendimento. No quarto capítulo, a teoria dos princípios é apresentada como uma teoria competente para resolver o problema da interpretação e aplicação racional dos direitos fundamentais, bem como a questão dos direitos não enumerados. Ainda nesse capítulo, defende-se a tese de que o reconhecimento de novos direitos fundamentais tem como procedimento mais geral a justificação de princípios que têm que ser levados em conta na aplicação coerente do sistema constitucional dos direitos a casos especialmente controversos. O capítulo final busca os critérios de reconhecimento de novos direitos fundamentais de acordo com a Constituição brasileira de 1988, afirmando que eles podem ser tomados como direitos implícitos ou direitos decorrentes do regime e dos princípios constitucionais.
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Boyle, Michael R. "Partial-enumeration for planar network interdiction problems." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1998. http://handle.dtic.mil/100.2/ADA343529.
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Keles, Gultekin. "Water Distribution Network Design By Partial Enumeration." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606816/index.pdf.
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Water distribution networks are being designed by traditional methods based on rules-of-thumb and personal experience of the designer. However, since there is no unique solution to any network design, namely there are various combinations of
pipes, pumps, tanks all of which satisfy the same pressure and velocity restrictions, it is most probable that the design performed by traditional techniques is not the optimum one.
This study deals how an optimization technique can be a useful tool for a designer during the design to find a solution. The method used within the study is the partial enumeration technique developed by Gessler. The technique is applied by a
commercially available software, i.e. WADISO SA. The study is focused on discrepancies between a network designed by traditional techniques and the same network designed by partial enumeration method. Attention is given to steps of enumeration, which are basically grouping of pipes, candidate pipe size and price function assignments, to demonstrate that the designers can control all the phases of optimization process. In this respect, special attention is given to price functions to show the effect of them on the result. The study also revealed that the cost of fitting materials cannot be included in the price function although it may have significant
effect in a system composed of closely located junctions.
The results obtained from this study are useful to show that although optimization methods do not provide a definite solution<br>partial enumeration method can assist designers to select the optimum system combination.
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Petersson, Anna. "Enumeration of spanning trees in simplicial complexes." Licentiate thesis, Uppsala universitet, Matematiska institutionen, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-138976.
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Soskova, Mariya Ivanova. "The Local Structure of the Enumeration Degrees." Thesis, University of Leeds, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491633.
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This thesis discusses properties of the local structure of the enumeration degrees. We begin with some historical background of the subject. vye give motivation for investigating the properties of the local structure ofthe enumeration degrees and discuss the basic concepts and methods used throughout the thesis. Chapter 2 presents evidence that the study of the structure of enumeration degrees can provide a richer understanding of the structure of the Thring degrees. We prove that -- -' - . there exists a II~ enumeration degree which is the bottom of a cone within which the II~ enumeration degrees cannot be cupped to O~. As a corollary we obtain a generalization of Harrington's non-splitting theorem for the ~g Thring degrees. Chapters 3 and 4 are dedicated to the study of properties, specific to the properly ~g enumeration degrees. In Chapter 3 we construct a properly ~g enumeration degree above which there is no splitting of O~. Degrees with this property can be used to define a filter in the local structure of the enumeration degrees that consists entirely of properly ~g enumeration degrees and O~. In Chapter 4 we strengthen the result obtained by Cooper, Li, Sorbi and Yang of the existence of a non-bounding enumeration degree by constructing a I-generic enumeration degree that does not bound a minimal pair. Degrees with this property· can be used to define an ideal consisting of properly ~g enumeration degrees and Oe. Chapters 5 and 6 concern the cupping properties of ~g enumeration degrees and the sub-classes of the ~g enumeration degrees related to the finite and w- levels of the Ershov hierarchy. In Chapter 5 we complement a result by Cooper, Sorbi and Yi by showing that every non-zero .6.g enumeration degree can be cupped by a partial low .6.g enumeration degree. On the other hand we show that one cannot computably list a sequence of degrees which contains a cupping partner for every .6.g enumeration degree. In Chapter 6 we concentrate on the smaller subclasses, where the situation improves. We prove that every non-zero w-c.e. enumeration degree can be cupped by a 3-c.e. enumeration degree and as the 3-c.e. enumeration degrees are computably enumerable this property constitutes a difference between the .6.g enumeration degrees and the w-c.e. enumeration degrees. Furthermore we establish a structural difference between the class of II~ enumeration degrees and the 3-c.e. enumeration degrees by proving that one cannot find a single Eg enumeration degree that cups every non-zero 3-c.e. enumeration degree to O~. Finally in Chapter 7 we show that the structure of the 3-c.e. enumeration degrees is far from trivial as there exists a Lachlan Il()n-spJ~tting pair with top a II~enuIlleration degree and bottom a 3-c.e. enumeration degree.
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Hays, Henry Charles Wilson. "Novel Systems for Bacterial Preservation and Enumeration." Thesis, University of Leeds, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491750.
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Much like books in a library, microbiological strains must be able to be stored over prolonged periods of time, while maintaining their condition and accessibility for the purposes ofresearch and reference. Many methods currently employed for the storing of microorganisms require highly specialized storage systems; substantial technical equipment; know-how and temperature controlled environments. Whilst these methods are effective, it is accepted that they can be expensive and technically demanding. Traditionally, methods ofevaluating novel storage techniques require the use of classical bacterial enumeration techniques, which are slow, labour intensive and expensive to automate. This work investigates the use of in-vivo bacterial bioluminescence as an alternative bacterial enumeration tool to aid the identification of novel preservatives and preservation formats for the quantitative and qualitative preservation of bacteria. The development of a cheap, simple, yet effective storage alternative to current preservation systems based on a novel self-drying concept, containing activated charcoal and sucrose protectant is reported. In addition, the evaluation of DNA transformed bacteria using plasmids containing lux gene cassettes was studied in order to assess transformation efficiencies in competent cells. Currently, competent cells are distributed and stored at very low temperatures in order to maintain their viability and competence, therefore, the demand for a technology that will alleviate the need for handling and storing of competent cells at sub-zero temperatures· is certainly present. However, methods employed in screening and developing new competent cell formats often rely on classical enumeration techniques. Therefore, the development of a fast screening tool in the form of bioluminescence would aid the development of novel competent cell formats. To this aim, a fast screening tool for the identification of positive competent cell. formulations was investigated.
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Peterson, Scott. "Analyzing the component processes of visual enumeration." Thesis, Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/28945.
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Venkataraman, Geetha. "Enumeration of the types of finite groups." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334908.
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Copestake, C. S. "The enumeration degrees of #SIGMA#2̲ sets." Thesis, University of Leeds, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.377069.
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Kim, Hyung Joo. "Electrochemical detection and enumeration of pathogenic bacteria." Thesis, King's College London (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244045.
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Hersh, Patricia (Patricia Lynn) 1973. "Decomposition and enumeration in partially ordered sets." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/85303.
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Yang, Bo-Yin. "Two enumeration problems about the Aztec diamonds." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/13937.
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Brown, Tova, and Tova Brown. "Asymptotics and Dynamics of Map Enumeration Problems." Diss., The University of Arizona, 2016. http://hdl.handle.net/10150/621078.
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We solve certain three-term recurrence relations for generating functions of map enumeration problems. These are combinatorial maps, an embedding of a graph into a surface in a particular way. The generating functions enumerate the maps according to an appropriate notion of a distance or height in the map. These problems were studied and the recurrence relations derived in [BDFG03] and [BM06].By viewing the three-term recurrence as giving a two-dimensional discrete dynamical system, these combinatorial problems are set in the context of discrete dynamical systems and integrable systems theory. The integrable nature of the system was made apparent by numerical study, and is confirmed by recognition that the recurrences are autonomous discrete Painleve-I equations. The autonomous discrete Painleve equations are known to be instances of the QRT Mapping, named for Quispel, Roberts, and Thompson [QRT88, QRT89], an integrable structure with explicitly-given invariant. Level sets of such invariants are in general elliptic curves, and thus orbits in the dynamical systems can be parametrized through elliptic functions. The solution to a recurrence relation for combinatorial generating functions is rigorously derived from the general elliptic parametrization of the dynamical system, as the combinatorial initial condition indicates that the combinatorial orbit actually lies on a stable manifold of a hyperbolic fixed point of the system. This special orbit thus lies on a separatrix of the system, which is given by a degeneration in the elliptic nature of the level sets of the invariant function. These solutions have a particularly nice algebraic form, which is seen to be a consequence of the degeneration of the elliptic parametrization. The framework and method are general, applicable to any combinatorial enumeration problem that arises with a similar QRT-type structure.
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JACQUARD, BENJAMIN. "Cartes et arbres : enumeration, generation et dessins." Palaiseau, Ecole polytechnique, 1997. http://www.theses.fr/1997EPXX0011.
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Ce document est la conclusion de travaux dans le domaine de la combinatoire et l'algorithmique des graphes planaires. L'objet principal de l'etude est la carte planaire qui est le plongement d'un graphe planaire dans la sphere. On distingue dans nos travaux deux axes principaux de recherche: la combinatoire bijective (4 chapitres) et la representation automatique de graphes (1 chapitre). Dans les chapitres 1 et 2, on etudie une famille d'arbres dont les sommets sont etiquetes par des entiers en suivant des regles reliant l'etiquette d'un nud a celles de ses fils. On les appelle arbres de description. On montre que pour certaines classes de type fixe, ces arbres sont en bijection avec differentes familles de cartes planaires: non-separable (similaire a 2-connexe), cubiques, cubiques 3-connexes, cartes euleriennes et cartes planaires quelconques. Nous construisons des equations fonctionnelles satisfaites par les series enumeratrices de ces differentes familles. Nous leur appliquons la methode quadratique et nous obtenons ainsi pour chaque famille la serie formelle solution. Nous montrons, dans le chapitre 3, que trois familles d'arbres sont en bijection les cartes planaires non-separables: les arbres de descriptions de type (1, 0), les arbres guingois et les arbres bien-etiquetes decroissants. Dans le dernier chapitre, notre objectif est de representer aussi lisiblement que possible une carte planaire dont on connait la description combinatoire sous forme de permutations. On applique un modele physique aux cartes afin de les dessiner. A partir d'un dessin initial obtenu grace a un algorithme de dessin sur une grille, on deplace les sommets de maniere a minimiser les interactions entre sommets et aretes. Nous montrons comment le choix du type de potentiel modifie l'apparence de la carte equilibree
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Choi-Lee, Seul Hee. "Enumeration des tableaux de Young semi-standard." Paris 11, 1992. http://www.theses.fr/1992PA112369.
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Nous considerons des tableaux de young semi-standard, c'est-a-dire strictement croissants en lignes et non decroissants en colonnes. En utilisant l'interpretation des determinants par des configurations de chemins de dyck ne se coupant pas, desainte-catherine et viennot (des-vie) ont donne une formule exacte pour le nombre de tableaux de young semi-standard de hauteur bornee ayant toutes leurs colonnes de hauteur paire. Nous generalisons le resultat de desainte-catherine et viennot, en tenant compte du nombre de colonnes de hauteur impaire. Nous donnons alors, par une preuve bijective, le nombre de tableaux de young semi-standard de hauteur bornee par 2k, ayant p colonnes de hauteur impaire et leurs entrees dans 1, 2,. . . , n. Nous trouvons egalement le nombre moyen de cases de tels tableaux semi-standard. Les fonctions generatrices de tels tableaux de young semi-standard peuvent s'exprimer comme la somme de determinants, chacun etant lui-meme la somme des valuations de configurations de chemins ne se coupant pas et ayant des pas elementaires nord et ouest dans un huitieme plan. Enfin, nous enumerons les chemins se composant de quatre pas elementaires: est, ouest, nord et sud, dans un huitieme plan et dans un quart de plan
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White, Gregory. "Enumeration-based algorithms in linear coding theory." Phd thesis, Faculty of Science, 2006. http://hdl.handle.net/2123/8084.
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Green, Shawn Jeffrey. "Extensions of the Power Group Enumeration Theorem." BYU ScholarsArchive, 2019. https://scholarsarchive.byu.edu/etd/7526.
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The goal of this paper is to develop extensions of Polya enumeration methods which count orbits of functions. De Bruijn, Harary, and Palmer all worked on this problem and created generalizations which involve permuting the codomain and domain of functions simultaneously. We cover their results and specifically extend them to the case where the group of permutations need not be a direct product of groups. In this situation, we develop a way of breaking the orbits into subclasses based on a characteristic of the functions involved. Additionally, we develop a formula for the number of orbits made up of bijective functions. As a final extension, we also expand the set we are acting on to be the set of all relations between finite sets. Then we show how to count the orbits of relations.
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Socci, Samanta. "Enumeration of polyominoes defined by combinatorial constraints." Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCC194.
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Après une partie introductive, où les définitions de base sont fournies et des motivations pour le travail sont présentées, la thèse se divise en deux chapitres. Le premier chapitre traite de certaines classes de polyominos, les polyominoes convexes dirigés et les polyominoes k-convexes. Dans la première partie du chapitre nous présentons une approche unifiée pour obtenir les séries génératrices des polyominoes convexes dirigés selon différentes statistiques. Dans la deuxième partie du chapitre nous traitons le problème de l'énumeration des polyominos k-convexes selon leur demi-périmètre. Ce problème est consideré difficile et il n'a été résolu que pour k= 1,2. Nous donnons une énumération complète, pour tout k, des sous classes des k-parallélogrammes et des polyominoes k-convexes dirigées. Le deuxième chapitre traite de polyominoes définis par des paires de permutations, appelles permutominoes. Nous introduisons une généralisation naturelle de la classe des permutominoes à toute dimension et nous presentons une approche d'énumération unifiée qui nous permets d'obtenir de nouveaux résultats et de retrouver des resultats déjà connus. Enfin, pour le cas de dimension deux, nous résolvons le problème ouvert de la caractérisation des paires de permutations associées à un permutomino convexe par colonne et nous donnons une preuve bijective de leur énumération<br>After an introductory part, where some basic definitions are provided and some motivations for the investigation are presented, the thesis is divided into two chapters. The first chapter concerns particular classes of polyominoes. After a presentation of the background and the introduction of notations, we introduce a unified approach to obtain generating functions for different statistics on directed convex polyominoes. The problem of counting k-convex polyominoes according to their semi-perimeter is a difficult problem: it is solved for k=1,2. In the last part of the first chapter we introduce two particular classes of k-convex polyominoes, namely k-parallelogram and directed k-convex polyominoes, and we solve completely the corresponding enumeration problem. The second chapter deals with permutominoes (polyominoes defined by pairs of permutations). It begins with a background and some classical enumerative results for particular permutominoes. We introduce a naturel generalization of permutominoes to any dimension and we obtain new enumerative results and other already known are recovered by a unified approach. Concerning the two dimensional case, we solve the open problem of the characterization of the pairs of permutations defining the column-convex permutominoes and we find a bijective proof for the number of directed column-convex permutominoes, that we know to be counted by factoriel numbers
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Ramachandran, Sridhar. "A reformulation-linearization based implicit enumeration algorithm for the rectilinear distance location-allocation problem." Thesis, This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-10102009-020147/.
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Raji, Mehrdad Ahmadzadeh. "High power residue codes over Galois rings and related lattices." Thesis, University of Exeter, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248091.
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Distler, Andreas [Verfasser]. "Classification and Enumeration of Finite Semigroups / Andreas Distler." Aachen : Shaker, 2010. http://d-nb.info/1081886196/34.
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