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Growth series
for graphs
Walter Liu and Richard Scott
Vol. 13 (2020), No. 5, 781–790
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Abstract |
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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. |
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Keywords
growth series, right-angled Coxeter groups, graphs
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Mathematical Subject Classification
Primary: 20F55
Secondary: 51M20
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Milestones
Received: 17 July 2019
Revised: 12 July 2020
Accepted: 11 August 2020
Published: 5 December 2020
Communicated by Kenneth S. Berenhaut
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Authors |
| Walter Liu | |
| Department of Mathematics and
Computer Science Santa Clara University Santa Clara, CA United States |
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| Richard Scott | |
| Department of Mathematics and
Computer Science Santa Clara University Santa Clara, CA United States |
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