The Poincar\'e Series of Coxeter Folding Subgroups
Combinatorics
2026-05-13 v1
Abstract
Folding subgroups give a way to realize non-simply-laced Coxeter groups as subgroups of simply-laced Coxeter groups. In this paper, we study how folding subgroups of finite and affine type are distributed length-wise by calculating the length generating function of the subgroup with respect the length of the ambient group. These generating functions have surprisingly nice formulas in terms of -integers and give rise to interesting combinatorial identities on polynomials involving length statistics of both the ambient group and folding subgroup.
Cite
@article{arxiv.2605.11057,
title = {The Poincar\'e Series of Coxeter Folding Subgroups},
author = {Camilo Augusto Villamil Chalarca and Edward Richmond},
journal= {arXiv preprint arXiv:2605.11057},
year = {2026}
}