Longest Alternating Subsequences of Permutations
نویسنده
چکیده
The length is(w) of the longest increasing subsequence of a permutation w in the symmetric group Sn 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 < c > d < · · · . For instance, the expected value (mean) of as(w) for w ∈ Sn is exactly (4n + 1)/6 if n ≥ 2.
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