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2020 Growth series for graphs
Walter Liu, Richard Scott
Involve 13(5): 781-790 (2020). DOI: 10.2140/involve.2020.13.781

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.

Citation

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Walter Liu. Richard Scott. "Growth series for graphs." Involve 13 (5) 781 - 790, 2020. https://doi.org/10.2140/involve.2020.13.781

Information

Received: 17 July 2019; Revised: 12 July 2020; Accepted: 11 August 2020; Published: 2020
First available in Project Euclid: 22 December 2020

MathSciNet: MR4190437
Digital Object Identifier: 10.2140/involve.2020.13.781

Subjects:
Primary: 20F55
Secondary: 51M20

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 5 • 2020
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