Formal conjugacy growth in graph products I

Laura Ciobanu; Susan Hermiller; Valentin Mercier

doi:10.4171/ggd/704

Formal conjugacy growth in graph products I

Laura Ciobanu, Susan Hermiller, Valentin Mercier

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Abstract

In this paper we give a recursive formula for the conjugacy growth series of a graph product in terms of the conjugacy growth and standard growth series of subgraph products. We also show that the conjugacy and standard growth rates in a graph product are equal provided that this property holds for each vertex group. All results are obtained for the standard generating set consisting of the union of generating sets of the vertex groups.

Original language	English
Pages (from-to)	427-457
Number of pages	31
Journal	Groups, Geometry, and Dynamics
Volume	17
Issue number	2
DOIs	https://doi.org/10.4171/ggd/704
Publication status	Published - 13 Mar 2023

Keywords

Conjugacy growth
graph product
right-angled Artin group
right-angled Coxeter group

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

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abstract = "In this paper we give a recursive formula for the conjugacy growth series of a graph product in terms of the conjugacy growth and standard growth series of subgraph products. We also show that the conjugacy and standard growth rates in a graph product are equal provided that this property holds for each vertex group. All results are obtained for the standard generating set consisting of the union of generating sets of the vertex groups.",

keywords = "Conjugacy growth, graph product, right-angled Artin group, right-angled Coxeter group",

author = "Laura Ciobanu and Susan Hermiller and Valentin Mercier",

note = "Funding Information: Funding. The first and third authors were supported by the Swiss National Science Foundation grant Professorship FN PP00P2-144681/1. The first author was also supported by EPSRC standard grant EP/R035814/1. The second author was supported by grants from the National Science Foundation (DMS-1313559) and the Simons Foundation (Collaboration Grant number 581433). The third author was also supported by the FCT Project UID/MAT/00297/2019 (Centro de Matem{\'a}tica e Aplica{\c c}{\~o}es) and the FCT Project PTDC/MHC-FIL/2583/2014. Publisher Copyright: {\textcopyright} 2023 European Mathematical Society.",

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KW - right-angled Coxeter group

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Formal conjugacy growth in graph products I

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