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Longest alternating subsequences of permutations

Richard P. Stanley
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Abstract

The length is(w) of the longest increasing subsequence of a permutation w in the symmetric group S_n has been the object of much investigation. We develop comparable results for the length as(w) of the longest alternating subsequence of w, where a sequence a,b,c,d,... is alternating if a>b d<.... For instance, the expected value (mean) of as(w) for w in S_n is exactly (4n+1)/6 if n>1.

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Richard P. Stanley. 2005-11-16. Longest alternating subsequences of permutations. https://arxiv.org/abs/math/0511419

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