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An Average Set Size Theorem

Published online by Cambridge University Press:  28 January 2003

DAVID REIMER
Affiliation:
Department of Mathematics, The College of New Jersey, Ewing, NJ 086280718, USA (e-mail: dreimer@tcnj.edu)

Abstract

In this paper we prove that, if a collection of sets [Ascr ] is union-closed, then the average set size of $\cal A is at least $\frac{1}{2}\log_2 (\vert{\cal A}\vert)$.

Type
Research Article
Copyright
2003 Cambridge University Press

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