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Strongly Primitive Salem Growth Polynomials for Right-Angled Coxeter Groups
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≥2, there are infinitely many connected K2d+1-free defining graphs whose full reciprocal-radius polynomial is an irreducible Salem polynomial of degree 2d. We also establish independence-polynomial obstructions for prescribed Salem polynomials, including a sharp first-coefficient bound a1≤−5. Finally, an elementary golden-ratio growth gap excludes Lehmer's number from the standard spherical growth rates of right-angled Coxeter groups.
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BibTeX
@misc{oh2026strongly,
title = {{Strongly Primitive Salem Growth Polynomials for Right-Angled Coxeter Groups}},
author = {Mingyu Oh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.29397},
eprint = {2606.29397},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.29397},
}
RIS
TY - UNPB
TI - Strongly Primitive Salem Growth Polynomials for Right-Angled Coxeter Groups
AU - Mingyu Oh
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2606.29397
UR - https://arxiv.org/abs/2606.29397
AB - 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≥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 establish independence-polynomial obstructions for prescribed Salem polynomials, including a sharp first-coefficient bound a_1≤−5. Finally, an elementary golden-ratio growth gap excludes Lehmer's number from the standard spherical growth rates of right-angled Coxeter groups.
ER -