Article contents
A generalization of Sperner's theorem
Part of:
Combinatorics
Published online by Cambridge University Press: 09 April 2009
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
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