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Uniform s-cross-intersecting families
release_kyw7mt2mlvgrbiivk6l6ifi7ae
by
Peter Frankl, Andrey Kupavskii
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as a article
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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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1611.07258v2
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