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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| Видавець: | Інститут прикладної математики і механіки НАН України |
|---|---|
| Дата: | 2012 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2012
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152238 |
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| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-152238 |
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dspace |
| spelling |
irk-123456789-1522382019-06-10T01:26:19Z Word length in symmetrized presentations of Thompson’s group F Horak, M. Johnson, A. Stonesifer, A. 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. 2012 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/152238 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Horak, M. Johnson, A. Stonesifer, A. |
| spellingShingle |
Horak, M. Johnson, A. Stonesifer, A. Word length in symmetrized presentations of Thompson’s group F Algebra and Discrete Mathematics |
| author_facet |
Horak, M. Johnson, A. Stonesifer, A. |
| author_sort |
Horak, M. |
| title |
Word length in symmetrized presentations of Thompson’s group F |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT horakm wordlengthinsymmetrizedpresentationsofthompsonsgroupf AT johnsona wordlengthinsymmetrizedpresentationsofthompsonsgroupf AT stonesifera wordlengthinsymmetrizedpresentationsofthompsonsgroupf |
| first_indexed |
2023-05-20T17:37:49Z |
| last_indexed |
2023-05-20T17:37:49Z |
| _version_ |
1796153729483800576 |