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A generalization of Sperner's theorem

Part of: Combinatorics

Published online by Cambridge University Press:  09 April 2009

D. E. Daykin ,
P. Frankl ,
C. Greene  and
A. J. W. Hilton
D. E. Daykin
Affiliation:
Department of Mathematics, The University of Reading, Reading, RG6 2AX, United Kingdom
P. Frankl
Affiliation:
Centre national de la recherche scientifique, 515 quai Anatole France, 75700 Paris, France
C. Greene
Affiliation:
Department of Mathematics, Haverford College, Haverford, Pennsylvania 19041, U.S.A.
A. J. W. Hilton
Affiliation:
Department of Mathematics, The University of Reading, Reading, RG6 2AX, United Kingdom
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Abstract

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Some generalizations of Sperner's theorem and of the LYM inequality are given to the case when A1,… At are t families of subsets of {1,…,m} such that a set in one family does not properly contain a set in another.

MSC classification

Secondary: 05A20: Combinatorial inequalities
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 4 , December 1981 , pp. 481 - 485
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Greene, C. and Kleitman, D. J., ‘Proof techniques in the theory of finite sets’, Studies in Combinatorics, edited by Rota, G.-C. (MAA Studies in Mathematics 17 (1978), 22–79).Google Scholar
[2]Kleitman, D. J., ‘On an extremal property of antichains in partial orders. The LYM property and some of its implications and applications’, Combinatorics edited by Hall, M. and van Lint, J. H., (Math. Centre Tracts 55, Amsterdam, 1974, 77–90).Google Scholar
[3]Sperner, E., ‘Ein Satz über Untermengen einer endlichen Menge’, Math. Z. 27 (1928), 544–548.CrossRefGoogle Scholar