A note on Puder's generalised co-growth formula for trees

Fuente: arXiv
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Autores principales: Li, Wenbo, Thomas, Joe
Formato: Preprint
Publicado: 2025
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author Li, Wenbo
Thomas, Joe
author_facet Li, Wenbo
Thomas, Joe
contents In this note, we prove a conjecture of Puder on an extension of the co-growth formula to any non-negative function defined on a bi-regular tree. A key component of our proof is the establishment of a resolvent identity, which serves as an operator version of the co-growth formula. We also provide a simpler proof of Puder's generalised co-growth formula for the regular tree.
format Preprint
id arxiv_https___arxiv_org_abs_2502_06372
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A note on Puder's generalised co-growth formula for trees
Li, Wenbo
Thomas, Joe
Combinatorics
05C05
In this note, we prove a conjecture of Puder on an extension of the co-growth formula to any non-negative function defined on a bi-regular tree. A key component of our proof is the establishment of a resolvent identity, which serves as an operator version of the co-growth formula. We also provide a simpler proof of Puder's generalised co-growth formula for the regular tree.
title A note on Puder's generalised co-growth formula for trees
topic Combinatorics
05C05
url https://arxiv.org/abs/2502.06372