English

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.

Keywords

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

R2 v1 2026-06-21T10:27:11.762Z