Word length in symmetrized presentations of Thompson’s group F

Thompson's groups F, T and Z were introduced by Richard Thompson in the 1960's in connection with questions in logic. They have since found applications in many areas of mathematics including algebra, logic and topology, and their metric properties with respect to standard generating sets...

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Published in:Algebra and Discrete Mathematics
Date:2012
Main Authors: Horak, M., Johnson, A., Stonesifer, A.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2012
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/152238
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Word length in symmetrized presentations of Thompson’s group F / M. Horak, A. Johnson, A. Stonesifer // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 185–216. — Бібліогр.: 12 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-152238
record_format dspace
spelling Horak, M.
Johnson, A.
Stonesifer, A.
2019-06-09T06:07:09Z
2019-06-09T06:07:09Z
2012
Word length in symmetrized presentations of Thompson’s group F / M. Horak, A. Johnson, A. Stonesifer // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 185–216. — Бібліогр.: 12 назв. — англ.
1726-3255
2010 MSC:20F65.
https://nasplib.isofts.kiev.ua/handle/123456789/152238
Thompson's groups F, T and Z were introduced by Richard Thompson in the 1960's in connection with questions in logic. They have since found applications in many areas of mathematics including algebra, logic and topology, and their metric properties with respect to standard generating sets have been studied heavily. In this paper, we introduce a new family of generating sets for F, which we denote as Zn, establish a formula for the word metric with respect to Z₁ and prove that F has dead ends of depth at least 2 with respect to Z₁.
This work was supported by NSF REU grant DMS 0453421.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Word length in symmetrized presentations of Thompson’s group F
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Word length in symmetrized presentations of Thompson’s group F
spellingShingle Word length in symmetrized presentations of Thompson’s group F
Horak, M.
Johnson, A.
Stonesifer, A.
title_short Word length in symmetrized presentations of Thompson’s group F
title_full Word length in symmetrized presentations of Thompson’s group F
title_fullStr Word length in symmetrized presentations of Thompson’s group F
title_full_unstemmed Word length in symmetrized presentations of Thompson’s group F
title_sort word length in symmetrized presentations of thompson’s group f
author Horak, M.
Johnson, A.
Stonesifer, A.
author_facet Horak, M.
Johnson, A.
Stonesifer, A.
publishDate 2012
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
description Thompson's groups F, T and Z were introduced by Richard Thompson in the 1960's in connection with questions in logic. They have since found applications in many areas of mathematics including algebra, logic and topology, and their metric properties with respect to standard generating sets have been studied heavily. In this paper, we introduce a new family of generating sets for F, which we denote as Zn, establish a formula for the word metric with respect to Z₁ and prove that F has dead ends of depth at least 2 with respect to Z₁.
issn 1726-3255
url https://nasplib.isofts.kiev.ua/handle/123456789/152238
citation_txt Word length in symmetrized presentations of Thompson’s group F / M. Horak, A. Johnson, A. Stonesifer // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 185–216. — Бібліогр.: 12 назв. — англ.
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