Year: 2026
Type: article
Abstract: Pólya trees are unlabeled rooted trees on n vertices. This paper gives a new way to generate Pólya trees, that conjecturally is very efficient. This allows comparing typical unlabeled and labeled tree statistics and comparing asymptotic theorems with “reality.” Our method is an application of the Burnside process, alternating two steps: from a labeled rooted tree, produce a uniform permutation fixing it; and from a permutation, produce a uniform labeled rooted tree fixed by it. This last step is linked to a product formula, refining Cayley’s, for the number of rooted labeled trees preserved by a given permutation.
Source: Forum of Mathematics Sigma
Authors: Laurent Bartholdi, Persi Diaconis
Institutions: University of Geneva, Stanford University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,650
OpenAlex ID: W7161163046