Year: 2026
Type: preprint
Abstract: We study standard spherical growth rates of right-angled Coxeter groups through the clique polynomial of the defining graph. We prove that every even degree at least four occurs as the degree of a strongly primitive Salem growth rate: for each $d \geq 2$, there are infinitely many connected $K_{2d+1}$-free defining graphs whose full reciprocal-radius polynomial is an irreducible Salem polynomial of degree $2d$. We also prove independence-polynomial obstructions for prescribed Salem polynomials, including a sharp first-coefficient bound $a_1 \leq -5$, and apply them to Lehmer's polynomial and its suspension multiples.
Source: arXiv (Cornell University)
Author: Oh, Mingyu
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166727296
Cites:
Cited by:
Related to: