Counting elements and geodesics in Thompson's group F

Elder, Murray, Fusy, Éric and Rechnitzer, Andrew (2010) Counting elements and geodesics in Thompson's group F. Journal of Algebra, 324 1: 102-121. doi:10.1016/j.jalgebra.2010.02.035

Author Elder, Murray
Fusy, Éric
Rechnitzer, Andrew
Title Counting elements and geodesics in Thompson's group F
Formatted title
Counting elements and geodesics in Thompson’s group F
Journal name Journal of Algebra   Check publisher's open access policy
ISSN 0021-8693
Publication date 2010-07-01
Sub-type Article (original research)
DOI 10.1016/j.jalgebra.2010.02.035
Volume 324
Issue 1
Start page 102
End page 121
Total pages 20
Editor M. Broue
Place of publication Maryland Heights, MO, U.S.A.
Publisher Academic Press
Collection year 2011
Language eng
Formatted abstract
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 (Guba, 2004). Indeed, numerical analysis of the series data strongly suggests that the growth rate of the group is exactly (3+√5)/2.
© 2010 Elsevier Inc.
Keyword Group growth function
Growth series
Geodesic growth series
Thompson's group F
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2011 Collection
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Citation counts: TR Web of Science Citation Count  Cited 1 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 3 times in Scopus Article | Citations
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Created: Sun, 27 Jun 2010, 00:05:16 EST