Fixed points of 321-avoiding permutations
Combinatorics
2019-04-02 v1 Probability
Abstract
We describe the distribution of the number and location of the fixed points of permu- tations that avoid the pattern 321 via a bijection with rooted plane trees on n + 1 vertices. Using the local limit theorem for Galton-Watson trees, we are able to give an explicit description of the limit of this distribution.
Cite
@article{arxiv.1607.08742,
title = {Fixed points of 321-avoiding permutations},
author = {Christopher Hoffman and Douglas Rizzolo and Erik Slivken},
journal= {arXiv preprint arXiv:1607.08742},
year = {2019}
}