Vol. 13, No. 5, 2020

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Growth series for graphs

Walter Liu and Richard Scott

Vol. 13 (2020), No. 5, 781–790
Abstract

Given a graph Γ, one can associate a right-angled Coxeter group W and a cube complex Σ on which W acts. By identifying W with the vertex set of Σ, one obtains a growth series for W defined as W(t) = wWt(w) , where (w) denotes the minimum length of an edge path in Σ from the vertex 1 to the vertex w. The series W(t) is known to be a rational function. We compute some examples and investigate the poles and zeros of this function.

Keywords
growth series, right-angled Coxeter groups, graphs
Mathematical Subject Classification
Primary: 20F55
Secondary: 51M20
Milestones
Received: 17 July 2019
Revised: 12 July 2020
Accepted: 11 August 2020
Published: 5 December 2020

Communicated by Kenneth S. Berenhaut
Authors
Walter Liu
Department of Mathematics and Computer Science
Santa Clara University
Santa Clara, CA
United States
Richard Scott
Department of Mathematics and Computer Science
Santa Clara University
Santa Clara, CA
United States