A new short proof of the EKR theorem

Details A new short proof of the EKR theorem A new short proof of the EKR theorem

2011-08-10

arxiv.org/abs/1108.2179v1

Mathematics

Combinatorics

4 pages

Scientific paper

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. Here a new proof is presented. It is even shorter than the classical proof of Katona using cyclic permutations, or the one found by Daykin applying the Kruskal-Katona theorem.

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