Some combinatorial problems in the theory of symmetric inverse semigroups
Let Xn={1,2,⋯,n} and let α:Domα⊆Xn→Imα⊆Xn be a (partial) transformation on Xn. On a partial one-one mapping of Xn the following parameters are defined: the height of α is h(α)=|Imα|, the right [left] waist of α is w+(α)=max(Imα)[w−(α)=min(Imα)], and fix of α is denoted by f(α), and defined by f(α)...
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| Дата: | 2010 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2010
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154602 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Some combinatorial problems in the theory of symmetric inverse semigroups / A. Umar // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 113–124. — Бібліогр.: 32 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-154602 |
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dspace |
| spelling |
irk-123456789-1546022019-06-16T01:32:00Z Some combinatorial problems in the theory of symmetric inverse semigroups Umar, A. Let Xn={1,2,⋯,n} and let α:Domα⊆Xn→Imα⊆Xn be a (partial) transformation on Xn. On a partial one-one mapping of Xn the following parameters are defined: the height of α is h(α)=|Imα|, the right [left] waist of α is w+(α)=max(Imα)[w−(α)=min(Imα)], and fix of α is denoted by f(α), and defined by f(α)=|{x∈Xn:xα=x}|. The cardinalities of some equivalences defined by equalities of these parameters on In, the semigroup of partial one-one mappings of Xn, and some of its notable subsemigroups that have been computed are gathered together and the open problems highlighted. 2010 Article Some combinatorial problems in the theory of symmetric inverse semigroups / A. Umar // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 113–124. — Бібліогр.: 32 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:20M18, 20M20, 05A10, 05A15 http://dspace.nbuv.gov.ua/handle/123456789/154602 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 |
Let Xn={1,2,⋯,n} and let α:Domα⊆Xn→Imα⊆Xn be a (partial) transformation on Xn. On a partial one-one mapping of Xn the following parameters are defined: the height of α is h(α)=|Imα|, the right [left] waist of α is w+(α)=max(Imα)[w−(α)=min(Imα)], and fix of α is denoted by f(α), and defined by f(α)=|{x∈Xn:xα=x}|. The cardinalities of some equivalences defined by equalities of these parameters on In, the semigroup of partial one-one mappings of Xn, and some of its notable subsemigroups that have been computed are gathered together and the open problems highlighted. |
| format |
Article |
| author |
Umar, A. |
| spellingShingle |
Umar, A. Some combinatorial problems in the theory of symmetric inverse semigroups Algebra and Discrete Mathematics |
| author_facet |
Umar, A. |
| author_sort |
Umar, A. |
| title |
Some combinatorial problems in the theory of symmetric inverse semigroups |
| title_short |
Some combinatorial problems in the theory of symmetric inverse semigroups |
| title_full |
Some combinatorial problems in the theory of symmetric inverse semigroups |
| title_fullStr |
Some combinatorial problems in the theory of symmetric inverse semigroups |
| title_full_unstemmed |
Some combinatorial problems in the theory of symmetric inverse semigroups |
| title_sort |
some combinatorial problems in the theory of symmetric inverse semigroups |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154602 |
| citation_txt |
Some combinatorial problems in the theory of symmetric inverse semigroups / A. Umar // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 113–124. — Бібліогр.: 32 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT umara somecombinatorialproblemsinthetheoryofsymmetricinversesemigroups |
| first_indexed |
2023-05-20T17:44:58Z |
| last_indexed |
2023-05-20T17:44:58Z |
| _version_ |
1796153999552937984 |