On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations
It is well-known [16] that the semigroup Tn of all total transformations of a given n-element set Xn is covered by its inverse subsemigroups. This note provides a short and direct proof, based on properties of digraphs of transformations, that every inverse subsemigroup of order-preserving transform...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2015 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2015
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/154250 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations / P. Catarino, P.M. Higgins, I. Levi// Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 162-171. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862679902148362240 |
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| author | Catarino, P. Higgins, P.M. Levi, I. |
| author_facet | Catarino, P. Higgins, P.M. Levi, I. |
| citation_txt | On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations / P. Catarino, P.M. Higgins, I. Levi// Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 162-171. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | It is well-known [16] that the semigroup Tn of all total transformations of a given n-element set Xn is covered by its inverse subsemigroups. This note provides a short and direct proof, based on properties of digraphs of transformations, that every inverse subsemigroup of order-preserving transformations on a finite chain Xn is a semilattice of idempotents, and so the semigroup of all order-preserving transformations of Xn is not covered by its inverse subsemigroups. This result is used to show that the semigroup of all orientation-preserving transformations and the semigroup of all orientation-preserving or orientation-reversing transformations of the chain Xn are covered by their inverse subsemigroups precisely when n≤3.
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| first_indexed | 2025-12-07T15:44:26Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-154250 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T15:44:26Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Catarino, P. Higgins, P.M. Levi, I. 2019-06-15T11:42:40Z 2019-06-15T11:42:40Z 2015 On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations / P. Catarino, P.M. Higgins, I. Levi// Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 162-171. — Бібліогр.: 18 назв. — англ. 1726-3255 2010 MSC:20M20, 05C25. https://nasplib.isofts.kiev.ua/handle/123456789/154250 It is well-known [16] that the semigroup Tn of all total transformations of a given n-element set Xn is covered by its inverse subsemigroups. This note provides a short and direct proof, based on properties of digraphs of transformations, that every inverse subsemigroup of order-preserving transformations on a finite chain Xn is a semilattice of idempotents, and so the semigroup of all order-preserving transformations of Xn is not covered by its inverse subsemigroups. This result is used to show that the semigroup of all orientation-preserving transformations and the semigroup of all orientation-preserving or orientation-reversing transformations of the chain Xn are covered by their inverse subsemigroups precisely when n≤3. The first author acknowledges support by the Portuguese Govern-ment through the Portuguese Foundation FCT under the project PEst-OE/MAT/UI4080/2014. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations Article published earlier |
| spellingShingle | On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations Catarino, P. Higgins, P.M. Levi, I. |
| title | On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations |
| title_full | On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations |
| title_fullStr | On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations |
| title_full_unstemmed | On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations |
| title_short | On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations |
| title_sort | on inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154250 |
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