Abstract
Meshalkin's theorem states that a class of ordered p-partitions of an n-set has at most max( n a 1,…,a p ) members if for each k the kth 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 Erdős's theorem about r-chain-free set families.
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