Asymptotic behavior of permutation records

Details Asymptotic behavior of permutation records Asymptotic behavior of permutation records

2008-04-02

arxiv.org/abs/0804.0446v3

Mathematics

Combinatorics

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

Scientific paper

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.

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