A note on Puder's generalised co-growth formula for trees
Combinatorics
2025-02-11 v1
Abstract
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.
Cite
@article{arxiv.2502.06372,
title = {A note on Puder's generalised co-growth formula for trees},
author = {Wenbo Li and Joe Thomas},
journal= {arXiv preprint arXiv:2502.06372},
year = {2025}
}