English

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