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A Sharp Bound for the Number of Sets that Pairwise Intersect at <Emphasis Type="Italic">k</Emphasis> Positive Values

Authors:	Email author" target="_blank">Hunter?S?Snevily Email author

Institution:	(1) Department of Mathematics, University of Idaho, Moscow, ID 83844, USA

Abstract:	In this paper we prove that if ${\user1{L}}$ is a set of k positive integers and {A ₁, ..., A _m} is a family of subsets of an n-element set satisfying ${\left\| {A_{i} \cap A_{j} } \right\|} \in {\user1{L}}$ , for all 1 i < j m, then $m \leqslant {\sum\nolimits_{i = 0}^k {{\left( {^{{n - 1}}_{i} } \right)}} }$ . The case k = 1 was proven 50 years ago by Majumdar.

Keywords:	05D05
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