Results 1 to 10 of about 58,072 (195)
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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Problems and Results in Extremal Combinatorics–V [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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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
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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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Problems in Extremal and Probabilistic Combinatorics. [PDF]
, 2012 Extremal combinatorics can be described as a subfield of combinatorics that studies the maximum or minimum size of discrete structures (such as graphs, set systems, or convex bodies) with certain properties. For example, a classical question of this kind is, ``what is the maximum number of edges that a triangle-free graph can have?''.
Lee, Choongbum
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Extremal Combinatorics and Universal Algorithms [PDF]
, 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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New results in extremal combinatorics
, 2021 Extremal problems, in general, ask for the optimal size of certain finite objects when some restrictions are imposed. In extremal combinatorics, a major field in combinatorics, one studies how global properties guarantee the existence of local substructures, or equivalently, how avoiding local substructures poses a constraint on global quantities.
Wong, Ching
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Probabilistic models for the analysis of inverse extremal problems in combinatorics [PDF]
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2022 In an inverse extremal problem for a combinatorial scheme with a given value of the objective function of the form of a certain extreme value of its characteristic, a probabilistic model is developed that ensures that this value is obtained in its ...
Nataliya Yu. Enatskaya
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Theory of combinatorial limits and extremal combinatorics [PDF]
In the past years, techniques from different areas of mathematics have been successfully applied in extremal combinatorics problems. Examples include applications of number theory, geometry and group theory in Ramsey theory and analytical methods to different problems in extremal combinatorics.\ud By providing an analytic point of view of many discrete
Lopes Martins, Taísa
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Several problems in extremal combinatorics [PDF]
This thesis presents three distinct contributions to extremal combinatorics. First, it resolves a conjecture by Bollobás, Brightwell, and Leader on the prevalence of unate k-SAT functions, proving that for all fixed k≥2, almost all k-SAT functions on n variables are unate (i.e., monotone after negating certain variables).
Dong, Dingding
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