A shorter, simpler, stronger proof of the Meshalkin-Hochberg-Hirsch bounds on componentwise antichains

Details A shorter, simpler, stronger proof of the Meshalkin-Hochberg-Hirsch bounds on componentwise antichains A shorter, simpler, stronger proof of the Meshalkin-Hochberg-Hirsch bounds on componentwise antichains

2001-12-07

arxiv.org/abs/math/0112068v3

J. Combin. Th. Ser. A 100 (2002), 196--199

Mathematics

Combinatorics

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Scientific paper

Meshalkin's theorem states that a class of ordered p-partitions of an n-set has at most $\max \binom{n}{a_1,...,a_p}$ members if for each k the k'th parts form an antichain. We give a new proof of this and the corresponding LYM inequality due to Hochberg and Hirsch, which is simpler and more general than previous proofs. It extends to a common generalization of Meshalkin's theorem and Erdos's theorem about r-chain-free set families.

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