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arXiv · 2401.01957

A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three

Jungeun Park·Douglas Rizzolo
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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.

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Jungeun Park, Douglas Rizzolo. 2024-01-03. A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three. https://arxiv.org/abs/2401.01957

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