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 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2015
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| 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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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations |
| spellingShingle |
On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations Catarino, P. Higgins, P.M. Levi, I. |
| title_short |
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_sort |
on inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations |
| author |
Catarino, P. Higgins, P.M. Levi, I. |
| author_facet |
Catarino, P. Higgins, P.M. Levi, I. |
| publishDate |
2015 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/154250 |
| 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. |
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| first_indexed |
2025-12-07T15:44:26Z |
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2025-12-07T15:44:26Z |
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