On Growth Functions of Coxeter Groups
Sebastian Bischof

TL;DR
This paper characterizes the finiteness of growth functions for 2-spherical Coxeter groups, showing specific conditions under which the growth function remains finite or becomes infinite based on the Coxeter diagram.
Contribution
It provides a complete characterization of when the growth function of 2-spherical Coxeter groups with complete diagrams is finite or infinite.
Findings
Finite growth function for q = n-1 in 2-spherical cases
Infinite growth function for q = n-2 with complete diagrams
Complete classification of growth function finiteness for these groups
Abstract
Let be a Coxeter system of rank and let be its growth function. It is known that holds for all . In this paper we will show that this still holds for , if is -spherical. Moreover, we will prove that holds for , if the Coxeter diagram of is the complete graph. These two results provide a complete characterization of the finiteness of the growth function in the case of -spherical Coxeter systems with complete Coxeter diagram.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Finite Group Theory Research · Graph theory and applications
