A new short proof of the EKR theorem

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Abstract

A family F is intersecting if F∩F ' ≠θ whenever F,F'∈F. Erdos, Ko, and Rado (1961) [6] showed that(1)|F|≤(n-1k-1) holds for an intersecting family of k-subsets of [n]:={1, 2, 3,, n}, n≥2k. For n>2k the only extremal family consists of all k-subsets containing a fixed element. Here a new proof is presented by using the Katona's shadow theorem for t-intersecting families. © 2012.

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Frankl, P., & Füredi, Z. (2012). A new short proof of the EKR theorem. Journal of Combinatorial Theory. Series A, 119(6), 1388–1390. https://doi.org/10.1016/j.jcta.2012.03.012

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