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A finite set covering theorem II

Published online by Cambridge University Press:  17 April 2009

Alan Brace  and
D.E. Daykin
Alan Brace
Affiliation:
University of Western Australia, Nedlands, Western Australia
D.E. Daykin
Affiliation:
University of Reading, Reading, England.
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Abstract

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Let n, s, t be integers with s > t > 1 and n > (t+2)2s–t–1. We prove that if n subsets of a set S with s elements have intersection I and union J then some t of them have intersection J and union J. The result is best possible.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 1 , February 1972 , pp. 19 - 24
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Brace, Alan and Daykin, D.E., “A finite set covering theorem”, Bull. Austral. Math. Soc. 5 (1971), 197–202.CrossRefGoogle Scholar