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A finite set covering theorem III

Published online by Cambridge University Press:  17 April 2009

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

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Let n, s, t be integers with s > t > 2. If a family of n different subsets of a set S, with s elements, has the properties, (i) each member belongs to a set of (t+1) members which together have union S, (ii) no member belongs to a set of t members which together have union S, then we prove that n ≤ (t+1)s−t−1. The result is best possible.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 3 , June 1972 , pp. 417 - 433
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