Results 11 to 20 of about 934 (196)
Reaction systems and extremal combinatorics properties
Theoretical Computer Science, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alberto Dennunzio +2 more
exaly +6 more sources
Information Inequalities via Submodularity and a Problem in Extremal Graph Theory [PDF]
Entropy, 2022 The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties.
Igal Sason
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PPP-Completeness and Extremal Combinatorics [PDF]
Electron. Colloquium Comput. Complex., 2022 Many classical theorems in combinatorics establish the emergence of substructures within sufficiently large collections of objects. Well-known examples are Ramsey's theorem on monochromatic subgraphs and the Erdős-Rado sunflower lemma. Implicit versions of the corresponding total search problems are known to be PWPP-hard; here "implici" means that the ...
Bourneuf, Romain +4 more
core +8 more sources
Problems and results in extremal combinatorics—II [PDF]
Discrete Mathematics, 2003 Extremal Combinatorics is among the most active topics in Discrete Mathematics, dealing with problems that are often motivated by questions in other areas, including Theoretical Computer Science and Information Theory. This paper contains a collection of problems and results in the area, including solutions or partial solutions to open problems ...
Alon, Noga, Noga Alon
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A path forward: Tropicalization in extremal combinatorics
Advances in Mathematics, 2022 Many important problems in extremal combinatorics can be be stated as proving a pure binomial inequality in graph homomorphism numbers, i.e., proving that hom$(H_1,G)^{a_1}\cdots$hom$(H_k,G)^{a_k}\geq$hom$(H_{k+1},G)^{a_{k+1}}\cdots$hom$(H_m,G)^{a_m}$ holds for some fixed graphs $H_1,\dots,H_m$ and all graphs $G$.
Grigoriy Blekherman, Annie Raymond
exaly +4 more sources
Graphical designs and extremal combinatorics
Linear Algebra and Its Applications, 2020 A graphical design is a proper subset of vertices of a graph on which many eigenfunctions of the Laplacian operator have mean value zero. In this paper, we show that extremal independent sets make extremal graphical designs, that is, a design on which the maximum possible number of eigenfunctions have mean value zero.
Konstantin Golubev
exaly +6 more sources
On the extremal combinatorics of the hamming space
Journal of Combinatorial Theory - Series A, 1995 In \(n\)-dimensional Hamming space three points are on a line, if they satisfy the triangle inequality with equality. The paper introduces the following problem: How many different points can be found in the Hamming space so that no three of them are on a line (that is they are in general position)? This maximum value is \(A(n)\). The paper surveys the
János Körner
exaly +4 more sources
Entropic Matroids and Their Representation [PDF]
Entropy, 2019 This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have support of cardinality p.
Emmanuel Abbe, Sophie Spirkl
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Substructure Densities in Extremal Combinatorics [PDF]
, 2021 One of the primary goals of combinatorial mathematics is to understand how an object's properties are influenced by the presence or multiplicity of a given substructure. Over time, it has become popular to highlight the asymptotic behaviour of objects by expressing results in terms of the density of substructures.
Chan, Timothy F. N.
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Extremal Combinatorics and Universal Algorithms
, 2018 In this dissertation we solve several combinatorial problems in different areas of mathematics: automata theory, combinatorics of partially ordered sets and extremal combinatorics. Firstly, we focus on some new automata that do not seem to have occurred much in the literature, that of solvability of mazes.
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