Relevant bibliographies by topics / Structural Combinatorics

Academic literature on the topic 'Structural Combinatorics'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Structural Combinatorics"

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Nesetril, Jaroslav. "ASPECTS OF STRUCTURAL COMBINATORICS (Graph Homomorphisms and Their Use)." Taiwanese Journal of Mathematics 3, no. 4 (December 1999): 381–423. http://dx.doi.org/10.11650/twjm/1500407157.

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Hofri, Micha, Chao Li, and Hosam Mahmoud. "ON THE COMBINATORICS OF BINARY SERIES-PARALLEL GRAPHS." Probability in the Engineering and Informational Sciences 30, no. 2 (March 9, 2016): 244–60. http://dx.doi.org/10.1017/s0269964815000364.

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Binary series-parallel (BSP) graphs have applications in transportation modeling, and exhibit interesting combinatorial properties. This work is limited to the second aspect. The BSP graphs of a given size – measured in edges – are enumerated. Under a uniform probability model, we investigate the asymptotic distribution of the order (number of vertices) and the asymptotic average length of a random walk (under different strategies) of large graphs of the same size. The systematic method throughout is to define the graphs, and the features we evaluate by a structural equation (equivalent to a regular expression). The structural equation is translated into an equation for a generating function, which is then analyzed.
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Bonin, Joseph E., and Anna de Mier. "Lattice path matroids: Structural properties." European Journal of Combinatorics 27, no. 5 (July 2006): 701–38. http://dx.doi.org/10.1016/j.ejc.2005.01.008.

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Hornfeck, Wolfgang. "On the combinatorics of crystal structures: number of Wyckoff sequences of given length." Acta Crystallographica Section A Foundations and Advances 78, no. 2 (February 4, 2022): 149–54. http://dx.doi.org/10.1107/s2053273321013565.

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A formula for the calculation of the number of Wyckoff sequences of a given length is presented, based on the combinatorics of multisets with finite multiplicities and a generating function approach, assuming a certain space-group type and taking into account the number of non-fixed and fixed Wyckoff positions, respectively. The formula is applied to the 44 distinguishable combinatorial types of the 230 space-group types. A comparison is made between the calculated frequencies of occurrence of Wyckoff sequences of given space-group type and length and the observed ones for actual crystal structures, as retrieved from the Pearson's Crystal Data Crystal Structure Database for Inorganic Compounds.
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Abramsky, Samson. "Structure and Power: an Emerging Landscape." Fundamenta Informaticae 186, no. 1-4 (August 30, 2022): 1–26. http://dx.doi.org/10.3233/fi-222116.

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In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer Science, but there may also be something of interest for model theorists and other logicians. The basic setting involves studying the category of relational structures via a resource-indexed family of adjunctions with some process category - which unfolds relational structures into tree-like forms, allowing natural resource parameters to be assigned to these unfoldings. One basic instance of this scheme allows us to recover, in a purely structural, syntax-free way: the Ehrenfeucht-Fraïssé game; the quantifier rank fragments of first-order logic; the equivalences on structures induced by (i) the quantifier rank fragments, (ii) the restriction of this fragment to the existential positive part, and (iii) the extension with counting quantifiers; and the combinatorial parameter of tree-depth (Nesetril and Ossona de Mendez). Another instance recovers the k-pebble game, the finite-variable fragments, the corresponding equivalences, and the combinatorial parameter of treewidth. Other instances cover modal, guarded and hybrid fragments, generalized quantifiers, and a wide range of combinatorial parameters. This whole scheme has been axiomatized in a very general setting, of arboreal categories and arboreal covers. Beyond this basic level, a landscape is beginning to emerge, in which structural features of the resource categories, adjunctions and comonads are reflected in degrees of logical and computational tractability of the corresponding languages. Examples include semantic characterisation and preservation theorems, and Lovász-type results on counting homomorphisms.
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Bowman, Chris, Anton Cox, Amit Hazi, and Dimitris Michailidis. "Path combinatorics and light leaves for quiver Hecke algebras." Mathematische Zeitschrift 300, no. 3 (September 29, 2021): 2167–203. http://dx.doi.org/10.1007/s00209-021-02829-0.

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AbstractWe recast the classical notion of “standard tableaux" in an alcove-geometric setting and extend these classical ideas to all “reduced paths" in our geometry. This broader path-perspective is essential for implementing the higher categorical ideas of Elias–Williamson in the setting of quiver Hecke algebras. Our first main result is the construction of light leaves bases of quiver Hecke algebras. These bases are richer and encode more structural information than their classical counterparts, even in the case of the symmetric groups. Our second main result provides path-theoretic generators for the “Bott–Samelson truncation" of the quiver Hecke algebra.
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Mykytenko, Victoriia, and Nataliia Sheludko. "Control of sustainable management according to multilevel combinatorics of homeostatic mechanisms." E3S Web of Conferences 255 (2021): 01029. http://dx.doi.org/10.1051/e3sconf/202125501029.

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The article aims to develop the methodological base for study and substantiation of homeostatic mechanisms of control of stability of managing systems in the conditions which is implemented according to the sustainable management concept. The article describes features of main types of homeostasis of managing systems (evolutionary, structural, resistant, system homeostasis), their hierarchical closed interrelation and inherent specific and predictive administrative properties. The following is herein substantiated: conditions of homeostasis generation and realization of specific effect of mechanisms and, respectively, regulators of adaptation of managing systems to external and internal transformations; directions and methods to form resistant, to institutional and resource restrictions, complementary managing complexes. The article states that the combinatorics of homeostasis controls includes stabilizing, inertial, adaptation, organizational and economic, kinematic, cybernetic, alarm, cognitive information, reparative, regenerative and other types of controls. It emphasizes that the complex of mechanisms to ensure self-regulating properties of systems must be focused on support of their adaptation abilities to external and internal transformations. Taking into account four-level structural hierarchy of homeostatic properties, the article substantiates the possibility of ensuring adequate design of regulators for their consolidation according to priority objects of tools and events localization.
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Rao, S. B., U. K. Sahoo, and V. Parameswaran. "Cycle stochastic graphs: Structural and forbidden graph characterizations." AKCE International Journal of Graphs and Combinatorics 17, no. 3 (April 21, 2020): 1076–80. http://dx.doi.org/10.1016/j.akcej.2020.01.004.

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Krüger, Ulrich. "Structural aspects of ordered polymatroids." Discrete Applied Mathematics 99, no. 1-3 (February 2000): 125–48. http://dx.doi.org/10.1016/s0166-218x(99)00129-8.

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Nešetřil, Jaroslav. "Structural Properties of Sparse Graphs." Electronic Notes in Discrete Mathematics 31 (August 2008): 247–51. http://dx.doi.org/10.1016/j.endm.2008.06.050.

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Dissertations / Theses on the topic "Structural Combinatorics"

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Ferra, Gomes de Almeida Girão António José. "Extremal and structural problems of graphs." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/285427.

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In this dissertation, we are interested in studying several parameters of graphs and understanding their extreme values. We begin in Chapter~$2$ with a question on edge colouring. When can a partial proper edge colouring of a graph of maximum degree $\Delta$ be extended to a proper colouring of the entire graph using an `optimal' set of colours? Albertson and Moore conjectured this is always possible provided no two precoloured edges are within distance $2$. The main result of Chapter~$2$ comes close to proving this conjecture. Moreover, in Chapter~$3$, we completely answer the previous question for the class of planar graphs. Next, in Chapter~$4$, we investigate some Ramsey theoretical problems. We determine exactly what minimum degree a graph $G$ must have to guarantee that, for any two-colouring of $E(G)$, we can partition $V(G)$ into two parts where each part induces a connected monochromatic subgraph. This completely resolves a conjecture of Bal and Debiasio. We also prove a `covering' version of this result. Finally, we study another variant of these problems which deals with coverings of a graph by monochromatic components of distinct colours. The following saturation problem proposed by Barrus, Ferrara, Vandenbussche, and Wenger is considered in Chapter~$5$. Given a graph $H$ and a set of colours $\{1,2,\ldots,t\}$ (for some integer $t\geq |E(H)|$), we define $sat_{t}(n, R(H))$ to be the minimum number of $t$-coloured edges in a graph on $n$ vertices which does not contain a rainbow copy of $H$ but the addition of any non-edge in any colour from $\{1,2,\ldots,t\}$ creates such a copy. We prove several results concerning these extremal numbers. In particular, we determine the correct order of $sat_{t}(n, R(H))$, as a function of $n$, for every connected graph $H$ of minimum degree greater than $1$ and for every integer $t\geq e(H)$. In Chapter~$6$, we consider the following question: under what conditions does a Hamiltonian graph on $n$ vertices possess a second cycle of length at least $n-o(n)$? We prove that the `weak' assumption of a minimum degree greater or equal to $3$ guarantees the existence of such a long cycle. We solve two problems related to majority colouring in Chapter~$7$. This topic was recently studied by Kreutzer, Oum, Seymour, van der Zypen and Wood. They raised the problem of determining, for a natural number $k$, the smallest positive integer $m = m(k)$ such that every digraph can be coloured with $m$ colours, where each vertex has the same colour as at most a proportion of $\frac{1}{k}$ of its out-neighbours. Our main theorem states that $m(k) \in \{2k-1, 2k\}$. We study the following problem, raised by Caro and Yuster, in Chapter~$8$. Does every graph $G$ contain a `large' induced subgraph $H$ which has $k$ vertices of degree exactly $\Delta(H)$? We answer in the affirmative an approximate version of this question. Indeed, we prove that, for every $k$, there exists $g(k)$ such that any $n$ vertex graph $G$ with maximum degree $\Delta$ contains an induced subgraph $H$ with at least $n-g(k)\sqrt{\Delta}$ vertices such that $V(H)$ contains at least $k$ vertices of the same degree $d \ge \Delta(H)-g(k)$. This result is sharp up to the order of $g(k)$. %Subsequently, we investigate a concept called $\textit{path-pairability}$. A graph is said to be path-pairable if for any pairing of its vertices there exist a collection of edge-disjoint paths routing the the vertices of each pair. A question we are concerned here asks whether every planar path pairable graph on $n$ vertices must possess a vertex of degree linear in $n$. Indeed, we answer this question in the affirmative. We also sketch a proof resolving an analogous question for graphs embeddable on surfaces of bounded genus. Finally, in Chapter~$9$, we move on to examine $k$-linked tournaments. A tournament $T$ is said to be $k$-linked if for any two disjoint sets of vertices $\{x_1,\ldots ,x_k\}$ and $\{y_1,\dots,y_k\}$ there are directed vertex disjoint paths $P_1,\dots, P_k$ such that $P_i$ joins $x_i$ to $y_i$ for $i = 1,\ldots, k$. We prove that any $4k$ strongly-connected tournament with sufficiently large minimum out-degree is $k$-linked. This result comes close to proving a conjecture of Pokrovskiy.
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Borenstein, Evan. "Additive stucture, rich lines, and exponential set-expansion." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29664.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009.
Committee Chair: Croot, Ernie; Committee Member: Costello, Kevin; Committee Member: Lyall, Neil; Committee Member: Tetali, Prasad; Committee Member: Yu, XingXing. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Tanigawa, Shinichi. "Combinatorial Rigidity and Generation of Discrete Structures." 京都大学 (Kyoto University), 2010. http://hdl.handle.net/2433/120806.

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Brignall, Robert. "Simplicity in relational structures and its application to permutation classes." Thesis, St Andrews, 2007. http://hdl.handle.net/10023/431.

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Rockney, Alissa Ann. "A Predictive Model Which Uses Descriptors of RNA Secondary Structures Derived from Graph Theory." Digital Commons @ East Tennessee State University, 2011. https://dc.etsu.edu/etd/1300.

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The secondary structures of ribonucleic acid (RNA) have been successfully modeled with graph-theoretic structures. Often, simple graphs are used to represent secondary RNA structures; however, in this research, a multigraph representation of RNA is used, in which vertices represent stems and edges represent the internal motifs. Any type of RNA secondary structure may be represented by a graph in this manner. We define novel graphical invariants to quantify the multigraphs and obtain characteristic descriptors of the secondary structures. These descriptors are used to train an artificial neural network (ANN) to recognize the characteristics of secondary RNA structure. Using the ANN, we classify the multigraphs as either RNA-like or not RNA-like. This classification method produced results similar to other classification methods. Given the expanding library of secondary RNA motifs, this method may provide a tool to help identify new structures and to guide the rational design of RNA molecules.
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Amiouny, Samir V. "Combinatorial mechanics." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/25576.

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Barnard, Kristen M. "Some Take-Away Games on Discrete Structures." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/44.

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The game of Subset Take-Away is an impartial combinatorial game posed by David Gale in 1974. The game can be played on various discrete structures, including but not limited to graphs, hypergraphs, polygonal complexes, and partially ordered sets. While a universal winning strategy has yet to be found, results have been found in certain cases. In 2003 R. Riehemann focused on Subset Take-Away on bipartite graphs and produced a complete game analysis by studying nim-values. In this work, we extend the notion of Take-Away on a bipartite graph to Take-Away on particular hypergraphs, namely oddly-uniform hypergraphs and evenly-uniform hypergraphs whose vertices satisfy a particular coloring condition. On both structures we provide a complete game analysis via nim-values. From here, we consider different discrete structures and slight variations of the rules for Take-Away to produce some interesting results. Under certain conditions, polygonal complexes exhibit a sequence of nim-values which are unbounded but have a well-behaved pattern. Under other conditions, the nim-value of a polygonal complex is bounded and predictable based on information about the complex itself. We introduce a Take-Away variant which we call “Take-As-Much-As-You-Want”, and we show that, again, nim-values can grow without bound, but fortunately they are very easily described for a given graph based on the total number of vertices and edges of the graph. Finally we consider Take-Away on a specific type of partially ordered set which we call a rank-complete poset. We have results, again via an analysis of nim-values, for Take-Away on a rank-complete poset for both ordinary play as well as misère play.
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Allen, Peter. "Finding combinatorial structures." Thesis, London School of Economics and Political Science (University of London), 2008. http://etheses.lse.ac.uk/60/.

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In this thesis we answer questions in two related areas of combinatorics: Ramsey theory and asymptotic enumeration. In Ramsey theory we introduce a new method for finding desired structures. We find a new upper bound on the Ramsey number of a path against a kth power of a path. Using our new method and this result we obtain a new upper bound on the Ramsey number of the kth power of a long cycle. As a corollary we show that, while graphs on n vertices with maximum degree k may in general have Ramsey numbers as large as ckn, if the stronger restriction that the bandwidth should be at most k is given, then the Ramsey numbers are bounded by the much smaller value. We go on to attack an old conjecture of Lehel: by using our new method we can improve on a result of Luczak, Rodl and Szemeredi [60]. Our new method replaces their use of the Regularity Lemma, and allows us to prove that for any n > 218000, whenever the edges of the complete graph on n vertices are two-coloured there exist disjoint monochromatic cycles covering all n vertices. In asymptotic enumeration we examine first the class of bipartite graphs with some forbidden induced subgraph H. We obtain some results for every H, with special focus on the cases where the growth speed of the class is factorial, and make some comments on a connection to clique-width. We then move on to a detailed discussion of 2-SAT functions. We find the correct asymptotic formula for the number of 2-SAT functions on n variables (an improvement on a result of Bollob´as, Brightwell and Leader [13], who found the dominant term in the exponent), the first error term for this formula, and some bounds on smaller error terms. Finally we obtain various expected values in the uniform model of random 2-SAT functions.
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Spiegel, Christoph. "Additive structures and randomness in combinatorics." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669327.

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Arithmetic Combinatorics, Combinatorial Number Theory, Structural Additive Theory and Additive Number Theory are just some of the terms used to describe the vast field that sits at the intersection of Number Theory and Combinatorics and which will be the focus of this thesis. Its contents are divided into two main parts, each containing several thematically related results. The first part deals with the question under what circumstances solutions to arbitrary linear systems of equations usually occur in combinatorial structures..The properties we will be interested in studying in this part relate to the solutions to linear systems of equations. A first question one might ask concerns the point at which sets of a given size will typically contain a solution. We will establish a threshold and also study the distribution of the number of solutions at that threshold, showing that it converges to a Poisson distribution in certain cases. Next, Van der Waerden’s Theorem, stating that every finite coloring of the integers contains monochromatic arithmetic progression of arbitrary length, is by some considered to be the first result in Ramsey Theory. Rado generalized van der Waerden’s result by characterizing those linear systems whose solutions satisfy a similar property and Szemerédi strengthened it to a statement concerning density rather than colorings. We will turn our attention towards versions of Rado’s and Szemerédi’s Theorem in random sets, extending previous work of Friedgut, Rödl, Rucin´ski and Schacht in the case of the former and of Conlon, Gowers and Schacht for the latter to include a larger variety of systems and solutions. Lastly, Chvátal and Erdo¿s suggested studying Maker-Breaker games. These games have deep connections to the theory of random structures and we will build on work of Bednarska and Luczak to establish the threshold for how much a large variety of games need to be biased in favor of the second player. These include games in which the first player wants to occupy a solution to some given linear system, generalizing the van der Waerden games introduced by Beck. The second part deals with the extremal behavior of sets with interesting additive properties. In particular, we will be interested in bounds or structural descriptions for sets exhibiting some restrictions with regards to either their representation function or their sumset. First, we will consider Sidon sets, that is sets of integers with pairwise unique differences. We will study a generalization of Sidon sets proposed very recently by Kohayakawa, Lee, Moreira and Rödl, where the pairwise differences are not just distinct, but in fact far apart by a certain measure. We will obtain strong lower bounds for such infinite sets using an approach of Cilleruelo. As a consequence of these bounds, we will also obtain the best current lower bound for Sidon sets in randomly generated infinite sets of integers of high density. Next, one of the central results at the intersection of Combinatorics and Number Theory is the Freiman–Ruzsa Theorem stating that any finite set of integers of given doubling can be efficiently covered by a generalized arithmetic progression. In the case of particularly small doubling, more precise structural descriptions exist. We will first study results going beyond Freiman’s well-known 3k–4 Theorem in the integers. We will then see an application of these results to sets of small doubling in finite cyclic groups. Lastly, we will turn our attention towards sets with near-constant representation functions. Erdo¿s and Fuchs established that representation functions of arbitrary sets of integers cannot be too close to being constant. We will first extend the result of Erdo¿s and Fuchs to ordered representation functions. We will then address a related question of Sárközy and Sós regarding weighted representation function.
La combinatòria aritmètica, la teoria combinatòria dels nombres, la teoria additiva estructural i la teoria additiva de nombres són alguns dels termes que es fan servir per descriure una branca extensa i activa que es troba en la intersecció de la teoria de nombres i de la combinatòria, i que serà el motiu d'aquesta tesi doctoral. La primera part tracta la qüestió de sota quines circumstàncies es solen produir solucions a sistemes lineals d’equacions arbitràries en estructures additives. Una primera pregunta que s'estudia es refereix al punt en que conjunts d’una mida determinada contindran normalment una solució. Establirem un llindar i estudiarem també la distribució del nombre de solucions en aquest llindar, tot demostrant que en certs casos aquesta distribució convergeix a una distribució de Poisson. El següent tema de la tesis es relaciona amb el teorema de Van der Waerden, que afirma que cada coloració finita dels nombres enters conté una progressió aritmètica monocromàtica de longitud arbitrària. Aquest es considera el primer resultat en la teoria de Ramsey. Rado va generalitzar el resultat de van der Waerden tot caracteritzant en aquells sistemes lineals les solucions de les quals satisfan una propietat similar i Szemerédi la va reforçar amb una versió de densitat del resultat. Centrarem la nostra atenció cap a versions del teorema de Rado i Szemerédi en conjunts aleatoris, ampliant els treballs anteriors de Friedgut, Rödl, Rucinski i Schacht i de Conlon, Gowers i Schacht. Per últim, Chvátal i Erdos van suggerir estudiar estudiar jocs posicionals del tipus Maker-Breaker. Aquests jocs tenen una connexió profunda amb la teoria de les estructures aleatòries i ens basarem en el treball de Bednarska i Luczak per establir el llindar de la quantitat que necessitem per analitzar una gran varietat de jocs en favor del segon jugador. S'inclouen jocs en què el primer jugador vol ocupar una solució d'un sistema lineal d'equacions donat, generalitzant els jocs de van der Waerden introduïts per Beck. La segona part de la tesis tracta sobre el comportament extrem dels conjunts amb propietats additives interessants. Primer, considerarem els conjunts de Sidon, és a dir, conjunts d’enters amb diferències úniques quan es consideren parelles d'elements. Estudiarem una generalització dels conjunts de Sidons proposats recentment per Kohayakawa, Lee, Moreira i Rödl, en que les diferències entre parelles no són només diferents, sinó que, en realitat, estan allunyades una certa proporció en relació a l'element més gran. Obtindrem límits més baixos per a conjunts infinits que els obtinguts pels anteriors autors tot usant una construcció de conjunts de Sidon infinits deguda a Cilleruelo. Com a conseqüència d'aquests límits, obtindrem també el millor límit inferior actual per als conjunts de Sidon en conjunts infinits generats aleatòriament de nombres enters d'alta densitat. A continuació, un dels resultats centrals a la intersecció de la combinatòria i la teoria dels nombres és el teorema de Freiman-Ruzsa, que afirma que el conjunt suma d'un conjunt finit d’enters donats pot ser cobert de manera eficient per una progressió aritmètica generalitzada. En el cas de que el conjunt suma sigui de mida petita, existeixen descripcions estructurals més precises. Primer estudiarem els resultats que van més enllà del conegut teorema de Freiman 3k-4 en els enters. Llavors veurem una aplicació d’aquests resultats a conjunts de dobles petits en grups cíclics finits. Finalment, dirigirem l’atenció cap a conjunts amb funcions de representació gairebé constants. Erdos i Fuchs van establir que les funcions de representació de conjunts arbitraris d’enters no poden estar massa a prop de ser constants. Primer estendrem el resultat d’Erdos i Fuchs a funcions de representació ordenades. A continuació, abordarem una pregunta relacionada de Sárközy i Sós sobre funció de representació ponderada.
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Burris, Christina Suzann. "Analytic Combinatorics Applied to RNA Structures." Thesis, Virginia Tech, 2018. http://hdl.handle.net/10919/83888.

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In recent years it has been shown that the folding pattern of an RNA molecule plays an important role in its function, likened to a lock and key system. γ-structures are a subset of RNA pseudoknot structures filtered by topological genus that lend themselves nicely to combinatorial analysis. Namely, the coefficients of their generating function can be approximated for large n. This paper is an investigation into the length-spectrum of the longest block in random γ-structures. We prove that the expected length of the longest block is on the order n - O(n^1/2). We further compare these results with a similar analysis of the length-spectrum of rainbows in RNA secondary structures, found in Li and Reidys (2018). It turns out that the expected length of the longest block for γ-structures is on the order the same as the expected length of rainbows in secondary structures.
Master of Science
Ribonucleic acid (RNA), similar in composition to well-known DNA, plays a myriad of roles within the cell. The major distinction between DNA and RNA is the nature of the nucleotide pairings. RNA is single stranded, to mean that its nucleotides are paired with one another (as opposed to a unique complementary strand). Consequently, RNA exhibits a knotted 3D structure. These diverse structures (folding patterns) have been shown to play important roles in RNA function, likened to a lock and key system. Given the cost of gathering data on folding patterns, little is known about exactly how structure and function are related. The work presented centers around building the mathematical framework of RNA structures in an effort to guide technology and further scientific discovery. We provide insight into the prevalence of certain important folding patterns.
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Books on the topic "Structural Combinatorics"

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Grynkiewicz, David J. Structural additive theory. Cham: Springer, 2013.

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Bonato, Anthony. The game of cops and robbers on graphs. Providence, R.I: American Mathematical Society, 2011.

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Matoušek, Jiří, Jaroslav Nešetřil, and Marco Pellegrini, eds. Geometry, Structure and Randomness in Combinatorics. Pisa: Scuola Normale Superiore, 2014. http://dx.doi.org/10.1007/978-88-7642-525-7.

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Bilbao, Jesús Mario. Cooperative Games on Combinatorial Structures. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-4393-0.

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Bilbao, Jesús Mario. Cooperative games on combinatorial structures. Boston: Kluwer Academic, 2000.

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Discrete structures and their interactions. Boca Raton: CRC Press/Taylor & Francis Group, 2013.

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1923-, Barlotti A., ed. Combinatorics '84: Proceedings of the International Conference on Finite Geometries and Combinatorial Structures, Bari, Italy, 24-29 September 1984. Amsterdam: North-Holland, 1986.

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Combinatorics '88 (1988 Ravello, Italy). Combinatorics '88: Proceedings of the International Conference on Incidence Geometries and Combinatorial Structures, Ravello, Italy, 23-28 May 1988. Rende, Italy: Mediterranean Press, 1991.

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International, Conference on Incidence Geometries and Combinatorial Structures (1988 Ravello Italy). Combinatorics '88: Proceedings of the International Conference on Incidence Geometries and Combinatorial Structures, Ravello, Italy, 23-28 May, 1988. Rende, Italy: Mediterranean Press, 1991.

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Goldberg, Leslie Ann. Efficient algorithms for listing combinatorial structures. Cambridge: Cambridge University Press, 1993.

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Book chapters on the topic "Structural Combinatorics"

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Korte, Bernhard, Rainer Schrader, and László Lovász. "Structural Properties." In Algorithms and Combinatorics, 57–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-58191-5_5.

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Korte, Bernhard, Rainer Schrader, and László Lovász. "Further Structural Properties." In Algorithms and Combinatorics, 77–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-58191-5_6.

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Molloy, Michael, and Bruce Reed. "The Structural Decomposition." In Algorithms and Combinatorics, 157–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-04016-0_15.

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Murota, Kazuo. "Introduction to Structural Approach — Overview of the Book." In Algorithms and Combinatorics, 1–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03994-2_1.

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Konstantinova, Elena. "On Some Structural Properties of Star and Pancake Graphs." In Information Theory, Combinatorics, and Search Theory, 472–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36899-8_23.

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Senthil Kumar, B. V., and Hemen Dutta. "Combinatorics." In Discrete Mathematical Structures, 39–134. Boca Raton, FL : CRC Press/Taylor & Francis Group, 2020. | Series: Mathematics and its applications : modelling, engineering, and social sciences: CRC Press, 2019. http://dx.doi.org/10.1201/9780429053689-2.

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Gerstein, Larry J. "Combinatorics." In Introduction to Mathematical Structures and Proofs, 191–275. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4265-3_5.

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Balling, Richard J. "Combinatorial Search." In Guide to Structural Optimization, 323–26. New York, NY: American Society of Civil Engineers, 1997. http://dx.doi.org/10.1061/9780784402207.ape.

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Golomb, Solomon W., and Andy Liu. "Combinatorial Structures." In Solomon Golomb’s Course on Undergraduate Combinatorics, 293–354. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72228-9_7.

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Backofen, Rolf, Gad M. Landau, Mathias Möhl, Dekel Tsur, and Oren Weimann. "Fast RNA Structure Alignment for Crossing Input Structures." In Combinatorial Pattern Matching, 236–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02441-2_21.

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Conference papers on the topic "Structural Combinatorics"

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Kolks, Giacomo, and Jürgen Weber. "Symmetric Single Rod Cylinders With Variable Piston Area? A Comprehensive Approach to the Right Solution." In BATH/ASME 2018 Symposium on Fluid Power and Motion Control. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/fpmc2018-8810.

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In contrast to rotational hydraulic displacement units, such as pumps or motors, conventional hydraulic cylinder actuators do not allow a continuous variation of their displacement quantity: the piston area is regarded constant. In order to adapt to varying load and velocity requirements in a load cycle under torque restrictions of the driving motor, cylinder drives often implement pumps with variable displacement. In this paper, cylinders with discretely variable effective piston area by means of variable circuitry of multi-chamber cylinders are discussed. Hydraulic symmetry or constant asymmetry of the hydraulic cylinder are traits of the cylinder that are required to fit the cylinder to pump structures for closed-circuit displacement control, as given in electro-hydrostatic compact drives (ECD). A methodology to generate all possible solutions of variable area cylinders under the constraint of ECD requirements is proposed. A comprehensive description of the solution space is given, based on combinatorics and solution of equation systems. The methodology dealing with abstract cylinder areas is backed up by a general approach to describe the mechanical cylinder design space to combine multiple cylinder areas in one structural unit. Examples for design of three and four area cylinders are given and results are discussed. The paper concludes with the development of a demonstrator design to allow experimental validation in a subsequent step.
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Zuo, Tanli, Yukun Qiu, and Wei-Shi Zheng. "Neighbor Combinatorial Attention for Critical Structure Mining." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/456.

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Graph convolutional networks (GCNs) have been widely used to process graph-structured data. However, existing GNN methods do not explicitly extract critical structures, which reflect the intrinsic property of a graph. In this work, we propose a novel GCN module named Neighbor Combinatorial ATtention (NCAT) to find critical structure in graph-structured data. NCAT attempts to match combinatorial neighbors with learnable patterns and assigns different weights to each combination based on the matching degree between the patterns and combinations. By stacking several NCAT modules, we can extract hierarchical structures that is helpful for down-stream tasks. Our experimental results show that NCAT achieves state-of-the-art performance on several benchmark graph classification datasets. In addition, we interpret what kind of features our model learned by visualizing the extracted critical structures.
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Doslic, Tomislav. "Secondary structures and some related combinatorial objects." In 1st Croatian Combinatorial Days. University of Zagreb Faculty of Civil Engineering, 2017. http://dx.doi.org/10.5592/co/ccd.2016.02.

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Martinjak, Ivica, and Ivana Zubac. "Secondary structures and some related combinatorial objects." In 1st Croatian Combinatorial Days. University of Zagreb Faculty of Civil Engineering, 2017. http://dx.doi.org/10.5592/co/ccd.2016.04.

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Tao, Terence. "Structure and Randomness in Combinatorics." In 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07). IEEE, 2007. http://dx.doi.org/10.1109/focs.2007.17.

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Tao, Terence. "Structure and Randomness in Combinatorics." In 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07). IEEE, 2007. http://dx.doi.org/10.1109/focs.2007.4389475.

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Li, Tuan-Jie, Wei-Qing Cao, and Jin-Kui Chu. "The Topological Representation and Detection of Isomorphism Among Geared Linkage Kinematic Chains." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5812.

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Abstract Proceeded from the topological characteristics of Geared Linkage Mechanisms (GLM) structure, a fully new graph, combinatorial graph, which can be used to describe the topological relationship in a Geared Linkage Kinematic Chain (GLKC), is firstly proposed. Then the corresponding matrix, combinatorial matrix, and the structural invariants of GLKC are presented. Based on the structural invariants, this paper establishes a systematic procedure for detecting isomorphism among GLKCs using the powers of combinatorial matrix. A computer program based on the procedure has been applied successfully for detecting isomorphism among both the planar kinematic chains as well as GLKCs.
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Krenn, Mario, Xuemei Gu, and Daniel Soltesz. "Questions on the Structure of Perfect Matchings Inspired by Quantum Physics." In 2nd Croatian Combinatorial Days. University of Zagreb Faculty of Civil Engineering, 2019. http://dx.doi.org/10.5592/co/ccd.2018.05.

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FENG, HAIHUI, and XIUYUN GUO. "θ*-PAIRS AND THE STRUCTURE OF FINITE GROUPS." In Proceedings of the Second International Congress in Algebra and Combinatorics. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812790019_0008.

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Flajolet, Philippe, Éric Fusy, and Carine Pivoteau. "Boltzmann Sampling of Unlabelled Structures." In 2007 Proceedings of the Fourth Workshop on Analytic Algorithmics and Combinatorics (ANALCO). Philadelphia, PA: Society for Industrial and Applied Mathematics, 2007. http://dx.doi.org/10.1137/1.9781611972979.5.

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Reports on the topic "Structural Combinatorics"

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Van Duren, Jeroen K., Carl Koch, Alan Luo, Vivek Sample, and Anil Sachdev. High-Throughput Combinatorial Development of High-Entropy Alloys For Light-Weight Structural Applications. Office of Scientific and Technical Information (OSTI), December 2017. http://dx.doi.org/10.2172/1413702.

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Gomes, Carla P. Bridging the Gap Between Theory and Practice: Structure and Randomization in Large Scale Combinatorial Search. Fort Belvoir, VA: Defense Technical Information Center, January 2012. http://dx.doi.org/10.21236/ada564027.

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