Results 11 to 20 of about 13,803 (191)
PPP-Completeness and Extremal Combinatorics
, 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 ...
Romain Bourneuf +4 more
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Extremal problems and the combinatorics of sumsets
, 2023 18 pages.
Melvyn B. Nathanson
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Universal limit theorems in graph coloring problems with connections to extremal combinatorics [PDF]
The Annals of Applied Probability, 2017 This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. These can be seen as generalizations of the birthday problem (what is the chance that there are two friends with the same birthday?).
Bhaswar B. Bhattacharya +2 more
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Reaction systems and extremal combinatorics properties
Theoretical Computer Science, 2015 Extremal combinatorics is the study of the size that a collection of objects must have in order to certainly satisfy a given property. Reaction systems are a recent formalism for computation inspired by chemical reactions. This work is a first contribution to the study of the behavior of large reaction systems by means of extremal combinatorics.
Alberto Dennunzio +2 more
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Extremal combinatorics, iterated pigeonhole arguments, and generalizations of PPP
, 2022 We study the complexity of computational problems arising from existence theorems in extremal combinatorics. For some of these problems, a solution is guaranteed to exist based on an iterated application of the Pigeonhole Principle. This results in the definition of a new complexity class within TFNP, which we call PLC (for "polynomial long choice ...
Amol Pasarkar +2 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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Optimal Probability Inequalities for Random Walks Related to Problems in Extremal Combinatorics [PDF]
SIAM Journal on Discrete Mathematics, 2012 Let S_n=X_1+...+X_n be a sum of independent symmetric random variables such that |X_{i}|\leq 1. Denote by W_n= _{1}+...+ _{n} a sum of independent random variables such that \prob{\eps_i = \pm 1} = 1/2. We prove that \mathbb{P}{S_{n} \in A} \leq \mathbb{P}{cW_k \in A}, where A is either an interval of the form [x, \infty) or just a single point.
Dainius Dzindzalieta +2 more
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Problems and results in extremal combinatorics—I
Discrete Mathematics, 2003 Noga Alon
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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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