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Counting common representatives and symmetric chain decompositions

Published online by Cambridge University Press:  14 November 2011

I. Anderson
I. Anderson
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
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Synopsis

We obtain lower bounds for the number of common systems of distinct representatives of two families of sets and the number of symmetric chain decompositions of certain ranked partially ordered sets.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 100 , Issue 1-2 , 1985 , pp. 151 - 155
Copyright
Copyright © Royal Society of Edinburgh 1985

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References

1Aigner, M.. Combinatorial theory (Berlin: Springer, 1980).Google Scholar
2Anderson, I.. Some problems in combinatorial number theory (Ph.D. thesis: University of Nottingham, 1967).Google Scholar
3Anderson, I.. On the divisors of a number. J. London Math. Soc. 43 (1968), 410–418.CrossRefGoogle Scholar
4Baker, K. A.. A generalization of Sperner's lemma. J. Combinatorial Theory 6 (1969), 224–225.CrossRefGoogle Scholar
5Bruijn, N. G. de, Tengbergen, C. van E. and Kruyswijk, D.. On the set of divisors of a number. Nieuw Arch. Wisk. 23 (1952), 191–193.Google Scholar
6Ford, L. R. and Fulkerson, D. R.. Network flows and systems of representatives. Canad. J. Math. 10 (1958), 78–84.CrossRefGoogle Scholar
7Greene, C. and Kleitman, D. J.. Proof techniques in the theory of finite sets. Studies in combinatorics, ed. Rota, G. C., pp. 22–79 (Providence, R.I.: AMS, 1978).Google Scholar
8Griggs, J. R.. Sufficient conditions for a symmetric chain order. SIAM J. Appl. Math. 32 (1977), 807–809.CrossRefGoogle Scholar
9Hall, M.. Distinct representatives of subsets. Bull. Amer. Math. Soc. 54 (1948), 922–926.CrossRefGoogle Scholar
10Hall, P.. On representatives of subsets. J. London Math. Soc. 10 (1935), 26–30.CrossRefGoogle Scholar
11Harper, L. H.. The morphology of partially ordered sets. J. Combinatorial Theory A 17 (1974), 44–58.CrossRefGoogle Scholar
12Kleitman, D. J.. On an extremal property of antichains in partial orders. Combinatorics, ed. Hall, M. and Lint, J. H. van, pp. 77–90 (Math. Centre Tracts 55, Amsterdam 1974).Google Scholar
13Ostrand, P. A.. Systems of distinct representatives. J. Math. Anal. Applic. 32 (1970), 1–4.Google Scholar
14Perfect, H.. Remark on a criterion for common transversals. Glasgow Math. J. 10 (1969), 66–67.Google Scholar
15Rado, R.. On the number of systems of distinct representatives. J. London Math. Soc. 42 (1967), 107–109.Google Scholar