A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three
- Resource Type
- Working Paper
- Authors
- Park, Jungeun; Rizzolo, Douglas
- Source
- Subject
- Mathematics - Probability
Mathematics - Combinatorics
60C05, 60F05, 60J80
- Language
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.
Comment: 11 pages