The Shape of Random Pattern-Avoiding Permutations
Combinatorics
2013-12-02 v3 Probability
Abstract
We initiate the study of limit shapes for random permutations avoiding a given pattern. Specifically, for patterns of length 3, we obtain delicate results on the asymptotics of distributions of positions of numbers in the permutations. We view the permutations as 0-1 matrices to describe the resulting asymptotics geometrically. We then apply our results to obtain a number of results on distributions of permutation statistics.
Cite
@article{arxiv.1303.7313,
title = {The Shape of Random Pattern-Avoiding Permutations},
author = {Sam Miner and Igor Pak},
journal= {arXiv preprint arXiv:1303.7313},
year = {2013}
}
Comments
38 pages, 14 figures. Fixed typos, added references and acknowledgments