WebTheorem 1. Namely, we shall use the cycle method, a technique rst intro-duced by Katona [15] in his beautiful proof of the EKR Theorem; however, some di culties which are not present in [15] must be dealt with. Roughly speaking, we combine the shifting technique with a weighted (or probabilis- WebTheorem 1.3. Any 2-transitive group has the EKR-module property. This result was conjectured in [25, Conjecture 1.3]. We feel that this is the most general statement for all 2-transitive groups, in the context of EKR-type results. The theorem also gives information about the structure of the maximum
arXiv:1911.11252v3 [math.CO] 12 Jul 2024
WebThe classical Erd˝os-Ko-Rado (EKR) Theorem states that if we choose a family of subsets, each of size k, from a fixed set of size n (n>2k), then the largest possible pairwise intersecting family has size t = (n. −1. D. k. −1. We consider the probability that a randomly selected family of size t = t. n WebAug 10, 2011 · A new short proof of the EKR theorem. A family F is intersecting if any two members have a nonempty intersection. Erdos, Ko, and Rado showed that F \leq {n-1\choose k-1} holds for an intersecting family of k-subsets of [n]:= {1,2,3,...,n}, n\geq 2k. For n> 2k the only extremal family consists of all k-subsets containing a fixed element. guys in gym shorts blog
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WebIn mathematics, the Erdős–Ko–Rado theorem limits the number of sets in a family of sets for which every two sets have at least one element in common. Paul Erdős, Chao … WebFeb 1, 2024 · The celebrated Erd\H{o}s-Ko-Rado (EKR) theorem for Paley graphs (of square order) states that all maximum cliques are canonical in the sense that each maximum clique arises from the subfield ... WebApr 17, 2024 · Erdős-Ko-Rado Theorem is a seminal result in extremal combinatorics and has been proved by various methods (see a survey in ). There have been many results that have generalized EKR in various ways over the decades. The aim of this paper is to give a generalization of the EKR Theorem to non-uniform families with some extra conditions. guys in half shirts