Counting elements and geodesics in Thompson's group F

Elder, M; Fusy, E; Rechnitzer, A

Counting elements and geodesics in Thompson's group F

Elder, M

Fusy, E Rechnitzer, A

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Publication Type:: Journal Article
Citation:: Journal of Algebra, 2010, 324 (1), pp. 102 - 121
Issue Date:: 2010-01-01

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Field	Value	Language
dc.contributor.author	Elder, M https://orcid.org/0000-0002-2438-3945	en_US
dc.contributor.author	Fusy, E	en_US
dc.contributor.author	Rechnitzer, A	en_US
dc.date.issued	2010-01-01	en_US
dc.identifier.citation	Journal of Algebra, 2010, 324 (1), pp. 102 - 121	en_US
dc.identifier.issn	0021-8693	en_US
dc.identifier.uri	http://hdl.handle.net/10453/98176
dc.description.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 [16]). Indeed, numerical analysis of the series data strongly suggests that the growth rate of the group is exactly 3+√5/2. © 2010 Elsevier Inc.	en_US
dc.relation.ispartof	Journal of Algebra	en_US
dc.relation.isbasedon	10.1016/j.jalgebra.2010.02.035	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Counting elements and geodesics in Thompson's group F	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	324	en_US
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	324	en_US

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 [16]). Indeed, numerical analysis of the series data strongly suggests that the growth rate of the group is exactly 3+√5/2. © 2010 Elsevier Inc.

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http://hdl.handle.net/10453/98176