Elsevier

Theoretical Computer Science

Volume 307, Issue 3, 14 October 2003, Pages 493-502
Theoretical Computer Science

Union of shadows

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Abstract

Our aim in this note is to show that if A is a family of (k3) 3-sets then there are at least (k4) 4-sets that may be written as unions of two 2-sets in the shadow of A. This is the first non-trivial case of a more general conjecture about unions of shadows.

Keywords

Colexicographic order
r-set
Lower-shadow of a system
Shadow of a system

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Supported by NSF grant ITR 0225610 and DARPA grant F33615-01-C-1900.