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 |
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| Date: | 2012 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2012
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| 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| _version_ | 1862729778152341504 |
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| author | Horak, M. Johnson, A. Stonesifer, A. |
| author_facet | Horak, M. Johnson, A. Stonesifer, A. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T19:16:50Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-152238 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:16:50Z |
| publishDate | 2012 |
| publisher | Інститут прикладної математики і механіки НАН України |
| 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 |
| spellingShingle | Word length in symmetrized presentations of Thompson’s group F Horak, M. Johnson, A. Stonesifer, A. |
| title | 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_short | Word length in symmetrized presentations of Thompson’s group F |
| title_sort | word length in symmetrized presentations of thompson’s group f |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152238 |
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