Given a graph , one can associate a right-angled Coxeter group and a cube complex on which acts. By identifying with the vertex set of , one obtains a growth series for defined as , where denotes the minimum length of an edge path in from the vertex to the vertex . The series is known to be a rational function. We compute some examples and investigate the poles and zeros of this function.
"Growth series for graphs." Involve 13 (5) 781 - 790, 2020. https://doi.org/10.2140/involve.2020.13.781