Asymptotic behavior of permutation records
Combinatorics
2014-11-14 v3
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.
Cite
@article{arxiv.0804.0446,
title = {Asymptotic behavior of permutation records},
author = {Igor Kortchemski},
journal= {arXiv preprint arXiv:0804.0446},
year = {2014}
}
Comments
15 pages, 3 figures. v3: final version, to appear in Journal of Combinatorial Theory, Series A