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Some intersection and union theorems for several families of finite sets

Part of: Combinatorics

Published online by Cambridge University Press:  26 February 2010

A. J. W. Hilton
A. J. W. Hilton
Affiliation:
Department of Mathematics, The University of Reading, England.
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Extract

In this paper we prove two analogues of the following theorem:

If is a collection of distinct subsets of {1, …, m} such that , i ≠ j ⇒ Ai ∩ Aj ≠ ∅, Ai ∪ Aj ≠ {1, …, m} then .

MSC classification

Secondary: 05A20: Combinatorial inequalities
Type
Research Article
Information
Mathematika , Volume 25 , Issue 1 , June 1978 , pp. 125 - 128
Copyright
Copyright © University College London 1978

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References

1.Brace, A. and Daykin, D. E.. “Sperner type theorems for finite sets”, Proc. Oxford Conf. on Combinatorics, 1972, I.M.A., eds. Welsh, D. J. A. and Woodall, D. R., 18–37.Google Scholar
2.Daykin, D. E. and Lovasz, L.. “The number of values of a Boolean function”, J. London Math. Soc, (2) 12 (1976), 225–230.CrossRefGoogle Scholar
3.Erdös, P., Herzog, M. and Schonheim, J.. “An extremal problem on the set of noncoprime divisors of an integer”, Israel J. Math. (1970), 408–412.Google Scholar
4.Erdös, P., Ko, Chao and Rado, R.. “Intersection theorems for systems of finite sets”, Quart. J. Math. (Oxford) (2), 12 (1961), 313–320.Google Scholar
5.Hilton, A. J. W.. “A theorem on finite sets”, Quart. J. Math. (Oxford) (2), 27 (1976), 33–36.Google Scholar
6.Schönheim, J.. “On a problem of Daykin concerning intersecting families of sets”, Proc. British Comb. Conf. 1973, L.M.S. Lecture Note Series 13, McDonough, T. P. and Mavron, V. C. (eds.), 139–140.Google Scholar
7.Seymour, P. D.. “On incomparable families of sets”, Mathematika, 20 (1973), 208–209.Google Scholar