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Asymptotic behavior of permutation records

Name: Asymptotic behavior of permutation records
Creator: Igor Kortchemski
Keywords: Independent random variables, Computational Theory and Mathematics, FOS: Mathematics, Records, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), 0102 computer and information sciences, 0101 mathematics, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Aug 2009Embargo end date: 01 Jan 2008Publisher:Elsevier BVJournal:Journal of Combinatorial Theory, Series A, volume 116, pages 1,154-1,166 (issn: 0097-3165,

Authors: Igor Kortchemski;

doi: 10.1016/j.jcta.2009.03.003 , 10.48550/arxiv.0804.0446

arXiv: http://arxiv.org/abs/0804.0446

Asymptotic behavior of permutation records

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Abstract

We study the asymptotic behavior of two statistics defined on the symmetric group S_n when n tends to infinity: the number of elements of S_n having k records, and the number of elements of S_n for which the sum of the positions of their records is k. We use a probabilistic argument to show that the scaled asymptotic behavior of these statistics can be described by remarkably simple functions.

15 pages, 3 figures. v3: final version, to appear in Journal of Combinatorial Theory, Series A

Related Organizations

École Normale Supérieure
France

Keywords

Independent random variables, Computational Theory and Mathematics, FOS: Mathematics, Records, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Scaled asymptotic behavior, Stirling numbers, Theoretical Computer Science

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