On the Limiting Distribution for the Longest Alternating Sequence in a Random Permutation

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dc.creatorWidom, Harold
dc.date2005-11-21
dc.date.accessioned2026-07-07T06:51:34Z
dc.date.available2026-07-07T06:51:34Z
dc.descriptionRecently Richard Stanley initiated a study of the distribution of the length as(w) of the longest alternating subsequence in a random permutation w from the symmetric group $S_n$. Among other things he found an explicit formula for the generating function (on n and k) for the probability that as(w) is at most k and conjectured that the distribution, suitably centered and normalized, tended to a Gaussian with variance 8/45. In this note we present a proof of the conjecture based on the generating function.
dc.descriptionLaTeX, 7 pages
dc.identifierhttps://arxiv.org/abs/math/0511533
dc.identifierhttp://arxiv.org/abs/math/0511533
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105026
dc.subjectCombinatorics
dc.subjectProbability
dc.subject05A15
dc.titleOn the Limiting Distribution for the Longest Alternating Sequence in a Random Permutation
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