A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three
Probability
2024-01-05 v1 Combinatorics
Abstract
We use local limits of Galton-Watson trees to establish local limit theorems for permutations conditioned to avoid a pattern of length three. In the case of 321-avoiding permutations our results resolve an open problem of Pinsky. In the other cases our results give new descriptions of the limiting objects in terms of size-biased Galton-Watson trees.
Keywords
Cite
@article{arxiv.2401.01957,
title = {A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three},
author = {Jungeun Park and Douglas Rizzolo},
journal= {arXiv preprint arXiv:2401.01957},
year = {2024}
}
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11 pages