Longest alternating subsequences of permutations

Details Longest alternating subsequences of permutations Longest alternating subsequences of permutations

2005-11-16

arxiv.org/abs/math/0511419v1

Mathematics

Combinatorics

19 pages

Scientific paper

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>bd<.... 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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