Counting elements and geodesics in Thompson's group F

Title: Counting elements and geodesics in Thompson's group F
Creator: Elder, Murray; Fusy, Éric; Rechnitzer, Andrew
Relation: Journal of Algebra Vol. 324, Issue 1, p. 102 - 121
Publisher Link: http://dx.doi.org/10.1016/j.jalgebra.2010.02.035
Publisher: Elsevier
Resource Type: journal article
Date: 2010
Description: We present two quite different algorithms to compute the number of elements in the sphere of radius n of Thompson's group F with standard generating set. The first of these requires exponential time and polynomial space, but additionally computes the number of geodesics and is generalisable to many other groups. The second algorithm requires polynomial time and space and allows us to compute the size of the spheres of radius n with n ≤ 1500. Using the resulting series data we find that the growth rate of the group is bounded above by 2.62167… . This is very close to Guba's lower bound of 3+√5 / 2. Indeed, numerical analysis of the series data strongly suggests that the growth rate of the group is exactly 3+√5 / 2.
Subject: group growth function; growth series; geodesic growth series; Thompson's group F
Identifier: http://hdl.handle.net/1959.13/926906
Identifier: uon:9982
Identifier: ISSN:0021-8693
Language: eng
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