Asymptotics of the Extremal Excedance Set Statistic
Combinatorics
2016-05-30 v2
Abstract
Answering a question of Clark and Ehrenborg (2010), we determine asymptotics for the number of permutations of size n that admit the most common excedance set. In fact, we provide a more general bivariate asymptotic using the multivariate asymptotic methods of R. Pemantle and M. C. Wilson. We also consider two applications of our main result. First, we determine asymptotics on the number of permutations of size n which simultaneously avoid the generalized patterns 21-34 and 34-21. Second, we determine asymptotics on the number of n-cycles that admit no stretching pairs.
Cite
@article{arxiv.1403.0691,
title = {Asymptotics of the Extremal Excedance Set Statistic},
author = {Rodrigo Ferraz de Andrade and Erik Lundberg and Brendan Nagle},
journal= {arXiv preprint arXiv:1403.0691},
year = {2016}
}
Comments
13 pages, 1 figure. Now published in the European Journal of Combinatorics