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 $d \geq 2$, 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.