Density results for uniform families

Abstract

A familyF of subsets is calledk-dense if there exists ak-element setA such that all 2k of its subsets can be obtained in the formAF for someFF. Best possible bounds are obtained for the maximum number of sets in notk-densek-partite families. This is a consequence of a new rank formula for inclusion matrices.

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Frankl, P., Watanabe, M. Density results for uniform families. Combinatorica 14, 115–119 (1994). https://doi.org/10.1007/BF01305954

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AMS subject classification code (1991)

  • 05 D 05
  • 15 A 03