Uniform s-cross-intersecting families release_kyw7mt2mlvgrbiivk6l6ifi7ae

by Peter Frankl, Andrey Kupavskii

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2017  

Abstract

In this paper we study a question related to the classical Erdős-Ko-Rado theorem, which states that any family of k-element subsets of the set [n] = {1,...,n} in which any two sets intersect, has cardinality at most n-1 k-1. We say that two non-empty families are A, B⊂[n] k are s-cross-intersecting, if for any A∈ A,B∈ B we have |A∩ B|> s. In this paper we determine the maximum of | A|+| B| for all n. This generalizes a result of Hilton and Milner, who determined the maximum of | A|+| B| for nonempty 1-cross-intersecting families.
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Date   2017-01-15
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arXiv  1611.07258v2
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