Asymptotic behavior of permutation records

Authors:
Igor Kortchemski
Affiliations:
École Normale Supérieure, 75005 Paris, France
Venue:
Journal of Combinatorial Theory Series A
Year:
2009

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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.