An algorithm for uniform generation of unlabeled trees (P\'olya trees), with an extension of Cayley's formula
Combinatorics
2024-11-27 v1 Group Theory
Probability
Abstract
P\'olya trees are rooted, unlabeled trees on vertices. This paper gives an efficient, new way to generate P\'olya trees. This allows comparing typical unlabeled and labeled tree statistics and comparing asymptotic theorems with `reality'. Along the way, we give a product formula for the number of rooted labeled trees preserved by a given automorphism; this refines Cayley's formula.
Cite
@article{arxiv.2411.17613,
title = {An algorithm for uniform generation of unlabeled trees (P\'olya trees), with an extension of Cayley's formula},
author = {Laurent Bartholdi and Persi Diaconis},
journal= {arXiv preprint arXiv:2411.17613},
year = {2024}
}