Strong Versions of Sperner’s Theorem

Document Type

Journal Article

Role

Author

Standard Number

0097-3165

Journal Title

Journal of Combinatorial Theory, Series A

Volume

20

Issue

1

First Page

80

Last Page

88

Publication Date

1976

Abstract

A procedure for partitioning the collection of divisors of an integer into symmetric chains is described and analyzed in detail. As a consequence, several strengthenings of Sperner's theorem are obtained. The algorithm also leads to elementary combinatorial proofs of a number of results on lattice paths and plane partitions.

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