Regular Intersecting Families

09/29/2017

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by   Ferdinand Ihringer, et al.

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We call a family of sets intersecting, if any two sets in the family intersect. In this paper we investigate intersecting families F of k-element subsets of [n]:={1,..., n}, such that every element of [n] lies in the same (or approximately the same) number of members of F. In particular, we show that we can guarantee |F| = o(n-1 k-1) if and only if k=o(n).