Dissertations / Theses on the topic 'Lattices and Combinatorics'
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Xin, Yuxin. "Strongly Eutactic Lattices From Vertex Transitive Graphs." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/cmc_theses/2171.
Full textGoodwin, Michelle. "Lattices and Their Application: A Senior Thesis." Scholarship @ Claremont, 2016. http://scholarship.claremont.edu/cmc_theses/1317.
Full textUsatine, Jeremy. "Arithmetical Graphs, Riemann-Roch Structure for Lattices, and the Frobenius Number Problem." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/57.
Full textAlexander, Matthew R. "Combinatorial and Discrete Problems in Convex Geometry." Kent State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1508949236617778.
Full textKrohne, Edward. "Continuous Combinatorics of a Lattice Graph in the Cantor Space." Thesis, University of North Texas, 2016. https://digital.library.unt.edu/ark:/67531/metadc849680/.
Full textHeuer, Manuela. "Combinatorial aspects of root lattices and words." Thesis, Open University, 2010. http://oro.open.ac.uk/24046/.
Full textYoon, Young-jin. "Characterizations of Some Combinatorial Geometries." Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc277894/.
Full textMelczer, Stephen. "Analytic Combinatorics in Several Variables : Effective Asymptotics and Lattice Path Enumeration." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEN013/document.
Full textThe field of analytic combinatorics, which studies the asymptotic behaviour ofsequences through analytic properties of their generating functions, has led to thedevelopment of deep and powerful tools with applications across mathematics and thenatural sciences. In addition to the now classical univariate theory, recent work in thestudy of analytic combinatorics in several variables (ACSV) has shown how to deriveasymptotics for the coefficients of certain D-finite functions represented by diagonals ofmultivariate rational functions. This thesis examines the methods of ACSV from acomputer algebra viewpoint, developing rigorous algorithms and giving the firstcomplexity results in this area under conditions which are broadly satisfied.Furthermore, this thesis gives several new applications of ACSV to the enumeration oflattice walks restricted to certain regions. In addition to proving several openconjectures on the asymptotics of such walks, a detailed study of lattice walk modelswith weighted steps is undertaken
Davis, Brian. "Lattice Simplices: Sufficiently Complicated." UKnowledge, 2019. https://uknowledge.uky.edu/math_etds/60.
Full textGay, Joël. "Representation of Monoids and Lattice Structures in the Combinatorics of Weyl Groups." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS209/document.
Full textAlgebraic combinatorics is the research field that uses combinatorial methods and algorithms to study algebraic computation, and applies algebraic tools to combinatorial problems. One of the central topics of algebraic combinatorics is the study of permutations, interpreted in many different ways (as bijections, permutation matrices, words over integers, total orders on integers, vertices of the permutahedron…). This rich diversity of perspectives leads to the following generalizations of the symmetric group. On the geometric side, the symmetric group generated by simple transpositions is the canonical example of finite reflection groups, also called Coxeter groups. On the monoidal side, the simple transpositions become bubble sort operators that generate the 0-Hecke monoid, whose algebra is the specialization at q=0 of Iwahori’s q-deformation of the symmetric group. This thesis deals with two further generalizations of permutations. In the first part of this thesis, we first focus on partial permutations matrices, that is placements of pairwise non attacking rooks on a n by n chessboard, simply called rooks. Rooks generate the rook monoid, a generalization of the symmetric group. In this thesis we introduce and study the 0-Rook monoid, a generalization of the 0-Hecke monoid. Its algebra is a proper degeneracy at q = 0 of the q-deformed rook monoid of Solomon. We study fundamental monoidal properties of the 0-rook monoid (Green orders, lattice property of the R-order, J-triviality) which allow us to describe its representation theory (simple and projective modules, projectivity on the 0-Hecke monoid, restriction and induction along an inclusion map).Rook monoids are actually type A instances of the family of Renner monoids, which are completions of the Weyl groups (crystallographic Coxeter groups) for Zariski’s topology. In the second part of this thesis we extend our type A results to define and give a presentation of 0-Renner monoids in type B and D. This also leads to a presentation of the Renner monoids of type B and D, correcting a misleading presentation that appeared earlier in the litterature. As in type A we study the monoidal properties of the 0-Renner monoids of type B and D : they are still J-trivial but their R-order are not lattices anymore. We study nonetheless their representation theory and the restriction of projective modules over the corresponding 0-Hecke monoids. The third part of this thesis deals with different generalizations of permutations. In a recent series of papers, Châtel, Pilaud and Pons revisit the algebraic combinatorics of permutations (weak order, Malvenuto-Reutenauer Hopf algebra) in terms of the combinatorics of integer posets. This perspective encompasses as well the combinatorics of quotients of the weak order such as binary trees, binary sequences, and more generally the recent permutrees of Pilaud and Pons. We generalize the weak order on the elements of the Weyl groups. This enables us to describe the order on vertices of the permutahedra, generalized associahedra and cubes in the same unified context. These results are based on subtle properties of sums of roots in Weyl groups, and actually fail for non-crystallographic Coxeter groups
Hedmark, Dustin g. "The Partition Lattice in Many Guises." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/48.
Full textMenix, Jacob Scott. "Properties of Functionally Alexandroff Topologies and Their Lattice." TopSCHOLAR®, 2019. https://digitalcommons.wku.edu/theses/3147.
Full textCampbell, Andre A. "Universal Cycles for Some Combinatorial Objects." Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/etd/1130.
Full textJung, JiYoon. "ANALYTIC AND TOPOLOGICAL COMBINATORICS OF PARTITION POSETS AND PERMUTATIONS." UKnowledge, 2012. http://uknowledge.uky.edu/math_etds/6.
Full textSjöstrand, Jonas. "Enumerative combinatorics related to partition shapes." Doctoral thesis, KTH, Matematik (Inst.), 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4298.
Full textÄmnet för denna avhandling är enumerativ kombinatorik tillämpad på tre olika objekt med anknytning till partitionsformer, nämligen tablåer, begränsade ord och bruhatintervall. Dom viktigaste vetenskapliga bidragen är följande. Artikel I: Låt tecknet av en standardtablå vara tecknet hos permutationen man får om man läser tablån rad för rad från vänster till höger, som en bok. En förmodan av Richard Stanley säjer att teckensumman av alla standardtablåer med n rutor är 2^[n/2]. Vi visar en generalisering av denna förmodan med hjälp av Robinson-Schensted-korrespondensen och ett nytt begrepp som vi kallar schacktablåer. Beviset bygger på ett anmärkningsvärt enkelt samband mellan tecknet hos en permutation pi och tecknen hos dess RS-motsvarande tablåer P och Q, nämligen sgn(pi)=(-1)^v sgn(P)sgn(Q), där v är antalet disjunkta vertikala dominobrickor som får plats i partitionsformen hos P och Q. Teckenobalansen hos en partitionsform definieras som teckensumman av alla standardtablåer av den formen. Som en ytterligare tillämpning av formeln för teckenöverföring ovan bevisar vi också en starkare variant av en annan förmodan av Stanley som handlar om viktade summor av kvadrerade teckenobalanser. Artikel II: Vi generaliserar några av resultaten i artikel I till skeva tablåer. Närmare bestämt undersöker vi hur teckenegenskapen överförs av Sagan och Stanleys skeva Robinson-Schensted-korrespondens. Resultatet är en förvånansvärt enkel generalisering av den vanliga ickeskeva formeln ovan. Som en tillämpning visar vi att vissa viktade summor av kvadrerade teckenobalanser blir noll, vilket leder till en generalisering av en variant av Stanleys andra förmodan. Artikel III: Följande specialfall av en förmodan av Loehr och Warrington bevisades av Ekhad, Vatter och Zeilberger: Det finns 10^n ord med summan noll av längd 5n i alfabetet {+3,-2} sådana att inget sammanhängande delord börjar med +3, slutar med -2 och har summan -2. Vi ger ett enkelt bevis för denna förmodan i dess ursprungliga allmännare utförande där 3 och 2 byts ut mot vilka som helst relativt prima positiva heltal a och b, 10^n byts ut mot ((a+b) över a)^n och 5n mot (a+b)n. För att göra detta formulerar vi problemet i termer av cylindriska latticestigar som kan tolkas som den sydöstra gränslinjen för vissa partitionsformer. Artikel IV: Vi karakteriserar dom permutationer pi sådana att elementen i det slutna bruhatintervallet [id,pi] i symmetriska gruppen motsvarar ickeslående tornplaceringar på ett skevt ferrersbräde. Dessa intervall visar sej vara precis dom vars flaggmångfalder är definierade av inklusioner, ett begrepp introducerat av Gasharov och Reiner. Karakteriseringen skapar en länk mellan poincarépolynom (ranggenererande funktioner) för bruhatintervall och q-tornpolynom, och vi kan beräkna poincarépolynomet för några särskilt intressanta intervall i dom ändliga weylgrupperna A_n och B_n. Uttrycken innehåller q-stirlingtal av andra sorten, och sätter man q=1 för grupp A_n så får man Kanekos poly-bernoullital.
QC 20100818
Cervetti, Matteo. "Pattern posets: enumerative, algebraic and algorithmic issues." Doctoral thesis, Università degli studi di Trento, 2003. http://hdl.handle.net/11572/311140.
Full textAllen, Emily. "Combinatorial Interpretations Of Generalizations Of Catalan Numbers And Ballot Numbers." Research Showcase @ CMU, 2014. http://repository.cmu.edu/dissertations/366.
Full textHaug, Nils Adrian. "Asymptotics and scaling analysis of 2-dimensional lattice models of vesicles and polymers." Thesis, Queen Mary, University of London, 2017. http://qmro.qmul.ac.uk/xmlui/handle/123456789/30706.
Full textBöhm, Walter, J. L. Jain, and Sri Gopal Mohanty. "On Zero avoiding Transition Probabilities of an r-node Tandem Queue - a Combinatorial Approach." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1992. http://epub.wu.ac.at/1356/1/document.pdf.
Full textSeries: Forschungsberichte / Institut für Statistik
Biro, Csaba. "Problems and results in partially ordered sets, graphs and geometry." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24719.
Full textCommittee Chair: Trotter, William T.; Committee Member: Duke, Richard A.; Committee Member: Randall, Dana; Committee Member: Thomas, Robin; Committee Member: Yu, Xingxing
Cervetti, Matteo. "Pattern posets: enumerative, algebraic and algorithmic issues." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/311152.
Full textChatel, Grégory. "Combinatoire algébrique liée aux ordres sur les arbres." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1136/document.
Full textThis thesis comes within the scope of algebraic combinatorics and studies of order structures on multiple tree families. We first look at the Tamari lattice on binary trees. This structure is obtained as a quotient of the weak order on permutations : we associate with each tree the interval of the weak order composed of its linear extensions. Note that there exists a bijection between intervals of the Tamari lattice and a family of poset that we callinterval-posets. The set of linear extensions of these posets is the union of the sets of linear extensions of the trees of the corresponding interval. We give a characterization of the posets satisfying this property and then we use this new family of objet on a large variety of applications. We first build another proof of the fact that the generating function of the intervals of the Tamari lattice satisfies a functional equation described by F. Chapoton. Wethen give a formula to count the number of trees smaller than or equal to a given tree in the Tamari order and in the $m$-Tamari order. We then build a bijection between interval-posets and flows that are combinatorial objects that F. Chapoton introduced to study the Pre-Lieoperad. To conclude, we prove combinatorially symmetry in the two parameters generating function of the intervals of the Tamari lattice. In the next part, we give a Cambrian generalization of the classical Hopf algebra of Loday-Ronco on trees and we explain their connection with Cambrian lattices. We first introduce our generalization of the planar binary tree Hopf algebra in the Cambrian world. We call this new structure the Cambrian algebra. We build this algebra as a Hopf sub algebra of a permutation algebra. We then study multiple properties of this objet such as its dual, its multiplicative basis and its freeness. We then generalize the Baxter algebra of S. Giraudo to the Cambrian world. We call this structure the Baxter-Cambrian Hopf algebra. The Baxter numbers being well-studied, we then explored their Cambrian counter parts, the Baxter-Cambrian numbers. To conclude this part, we give a generalization of the Cambrian algebra using a packed word algebra instead of a permutation algebra as a base for our construction. We call this new structure the Schröder-Cambrian algebra
Le, Tran Bach. "On k-normality and regularity of normal projective toric varieties." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31531.
Full textMeyer, Marie. "Polytopes Associated to Graph Laplacians." UKnowledge, 2018. https://uknowledge.uky.edu/math_etds/54.
Full textBureaux, Julien. "Méthodes probabilistes pour l'étude asymptotique des partitions entières et de la géométrie convexe discrète." Thesis, Paris 10, 2015. http://www.theses.fr/2015PA100160/document.
Full textThis thesis consists of several works dealing with the enumeration and the asymptotic behaviour of combinatorial structures related to integer partitions. A first work concerns partitions of large bipartite integers, which are a bidimensional generalization of integer partitions. Asymptotic formulæ are obtained in the critical regime where one of the numbers is of the order of magnitude of the square of the other number, and beyond this critical regime. This completes the results established in the fifties by Auluck, Nanda, and Wright. The second work deals with lattice convex chains in the plane. In a statistical model introduced by Sinaï, an exact integral representation of the partition function is given. This leads to an asymptotic formula for the number of chains joining two distant points, which involves the non trivial zeros of the Riemann zeta function. A detailed combinatorial analysis of convex chains is presented. It makes it possible to prove the existence of a limit shape for random convex chains with few vertices, answering an open question of Vershik. A third work focuses on lattice zonotopes in higher dimensions. An asymptotic equality is given for the logarithm of the number of zonotopes contained in a convex cone and such that the endings of the zonotope are fixed. A law of large numbers is established and the limit shape is characterized by the Laplace transform of the cone
Pons, Viviane. "Combinatoire algébrique liée aux ordres sur les permutations." Phd thesis, Université Paris-Est, 2013. http://tel.archives-ouvertes.fr/tel-00952773.
Full textGastineau, Nicolas. "Partitionnement, recouvrement et colorabilité dans les graphes." Thesis, Dijon, 2014. http://www.theses.fr/2014DIJOS014/document.
Full textOur research are about graph coloring with distance constraints (packing coloring) or neighborhood constraints (Grundy coloring). Let S={si| i in N*} be a non decreasing sequence of integers. An S-packing coloring is a proper coloring such that every set of color i is an si-packing (a set of vertices at pairwise distance greater than si). A graph G is (s1,... ,sk)-colorable if there exists a packing coloring of G with colors 1,... ,k. A Grundy coloring is a proper vertex coloring such that for every vertex of color i, u is adjacent to a vertex of color j, for each ji. These results allow us to determine S-packing coloring of these lattices for several sequences of integers. We examine a class of graph that has never been studied for S-packing coloring: the subcubic graphs. We determine that every subcubic graph is (1,2,2,2,2,2,2)-colorable and (1,1,2,2,3)-colorable. Few results are proven about some subclasses. Finally, we study the Grundy number of regular graphs. We determine a characterization of the cubic graphs with Grundy number 4. Moreover, we prove that every r-regular graph without induced square has Grundy number r+1, for r<5
Giuliani, Luca. "Extending the Moving Targets Method for Injecting Constraints in Machine Learning." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23885/.
Full textRamanan, Gurumurthi V. "Proof Of A Conjecture Of Frankl And Furedi And Some Related Theorems." Thesis, 1996. http://etd.iisc.ernet.in/handle/2005/1888.
Full textWeir, Brandon. "Homomorphic Encryption." Thesis, 2013. http://hdl.handle.net/10012/7264.
Full textVu, Xuan. "Analysis of necessary conditions for the optimal control of a train." 2006. http://arrow.unisa.edu.au:8081/1959.8/45958.
Full textNcambalala, Thokozani Paxwell. "Combinatorics of lattice paths." Thesis, 2014. http://hdl.handle.net/10539/15328.
Full textThis dissertation consists of ve chapters which deal with lattice paths such as Dyck paths, skew Dyck paths and generalized Motzkin paths. They never go below the horizontal axis. We derive the generating functions to enumerate lattice paths according to di erent parameters. These parameters include strings of length 2, 3, 4 and r for all r 2 f2; 3; 4; g, area and semi-base, area and semi-length, and semi-base and semi-perimeter. The coe cients in the series expansion of these generating functions give us the number of combinatorial objects we are interested to count. In particular 1. Chapter 1 is an introduction, here we derive some tools that we are going to use in the subsequent Chapters. We rst state the Lagrange inversion formula which is a remarkable tool widely use to extract coe cients in generating functions, then we derive some generating functions for Dyck paths, skew Dyck paths and Motzkin paths. 2. In Chapter 2 we use generating functions to count the number of occurrences of strings in a Dyck path. We rst derive generating functions for strings of length 2, 3, 4 and r for all r 2 f2; 3; 4; g, we then extract the coe cients in the generating functions to get the number of occurrences of strings in the Dyck paths of semi-length n. 3. In Chapter 3, Sections 3.1 and 3.2 we derive generating functions for the relationship between strings of lengths 2 and 3 and the relationship between strings of lengths 3 and 4 respectively. In Section 3.3 we derive generating functions for the low occurrences of the strings of lengths 2, 3 and 4 and lastly Section 3.4 deals with derivations of generating functions for the high occurrences of some strings . 4. Chapter 4, Subsection 4.1.1 deals with the derivation of the generating functions for skew paths according to semi-base and area, we then derive the generating functions according to area. In Subsection 4.1.2, we consider the same as in Section 4.1.1, but here instead of semi-base we use semi-length. The last section 4.2, we use skew paths to enumerate the number of super-diagonal bar graphs according to perimeter. 5. Chapter 5 deals with the derivation of recurrences for the moments of generalized Motzkin paths, in particular we consider those Motzkin paths that never touch the x-axis except at (0,0) and at the end of the path.
Dube, Nolwazi Mitchel. "Combinatorial properties of lattice paths." Thesis, 2017. http://hdl.handle.net/10539/23725.
Full textWe study a type of lattice path called a skew Dyck path which is a generalization of a Dyck path. Therefore we first introduce Dyck paths and study their enumeration according to various parameters such as number of peaks, valleys, doublerises and return steps. We study characteristics such as bijections with other combinatorial objects, involutions and statistics on skew Dyck paths. We then show enumerations of skew Dyck paths in relation to area, semi-base and semi-length. We finally introduce superdiagonal bargraphs which are associated with skew Dyck paths and enumerate them in relation to perimeter and area
GR2018
Ayyer, Arvind. "Statistical mechanics and combinatorics of some discrete lattice models." 2008. http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.17428.
Full textDziemiańczuk, Maciej. "Counting lattice paths." Doctoral thesis, 2015. https://depotuw.ceon.pl/handle/item/1719.
Full textŚcieżka kratowa to skończony ciąg punktów p0,p1,...,pn ze zbioru Z^2, natomiast segment ścieżki to różnica pi – p(i-1) dwóch kolejnych punktów ścieżki. W tej rozprawie badamy ścieżki pomiędzy dwoma ustalonymi punktami, dla których zbiór dozwolonych segmentów zawiera segment wertykalny (0,-1) oraz pewną przeliczalną liczbę segmentów niewertykalnych (1,k), gdzie k jest liczba całkowitą. Ścieżki te uogólniają dobrze znane z literatury tak zwane proste ścieżki skierowane (ang. simple directed lattice paths), które składają się jedynie z segmentów niewertykalnych.Niniejsza rozprawa podzielona jest na dwie części. W pierwszej części (Rozdział 2), pokazujemy, że pewne rodziny ścieżek z segmentami wertykalnymi możemy kodować za pomocą ważonych prostych ścieżek skierowanych. Zaprezentowany zostanie szereg rezultatów dla ogólnego przypadku, które zostaną następnie zastosowane dla trzech szczególnych rodzin ścieżek związanych ze ścieżkami Łukasiewicza, Raneya i Dycka.Druga część rozprawy (Rozdział 3) poświęcona jest badaniu pewnych własności multidrzew porządkowych, które definiuje się jako nieetykietowane ukorzenione drzewa, w których dodatkowo ustala się porządek synów oraz krawędziom przypisuje liczby naturalne. Zamiast zajmować się bezpośrednio tymi strukturami, pokażemy bijekcję pomiędzy drzewami porządkowymi a ścieżkami Raneya. Dzięki tej bijekcji otrzymany zostanie szereg kolejnych wyników dla multidrzew.
Ye, Lu. "Adsorbing staircase walks models of polymers in the square lattice /." 2005.
Find full textTypescript. Includes bibliographical references (leaves 99-102). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url%5Fver=Z39.88-2004&res%5Fdat=xri:pqdiss &rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR11932
Schwerdtfeger, Uwe [Verfasser]. "Combinatorial and probabilistic aspects of lattice path models = Kombinatorische und probabilistische Aspekte von Gitterwegmodellen / vorgelegt von Uwe Schwerdtfeger." 2010. http://d-nb.info/1003803881/34.
Full textIrvine, Veronika. "Lace tessellations: a mathematical model for bobbin lace and an exhaustive combinatorial search for patterns." Thesis, 2016. http://hdl.handle.net/1828/7495.
Full textGraduate
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(8422929), Ivan Chio. "Some Connections Between Complex Dynamics and Statistical Mechanics." Thesis, 2020.
Find full textPoirier, Antoine. "Les progressions arithmétiques dans les nombres entiers." Thèse, 2012. http://hdl.handle.net/1866/6931.
Full textThe subject of this thesis is the study of arithmetic progressions in the integers. Precisely, we are interested in the size v(N) of the largest subset of the integers from 1 to N that contains no 3 term arithmetic progressions. Therefore, we will construct a large subset of integers with no such progressions, thus giving us a lower bound on v(N). We will begin by looking at the proofs of all the significant lower bounds obtained on v(N), then we will show another proof of the best lower bound known today. For the proof, we will consider points on a large d-dimensional annulus, and count the number of integer points inside that annulus and the number of arithmetic progressions it contains. To obtain bounds on those quantities, it will be interesting to look at the theory behind counting lattice points in high dimensional spheres, which is the subject of the last section.
Siegel, Angela Annette. "ON THE STRUCTURE OF GAMES AND THEIR POSETS." Thesis, 2011. http://hdl.handle.net/10222/13499.
Full text