Asymptotic behavior of permutation records
arXiv:0804.0446 · doi:10.1016/j.jcta.2009.03.003
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