Some combinatorial problems in the theory of partial transformation semigroups
Let Xn = {1,2,…,n}. On a partial transformation α : Dom α ⊆ Xn → Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is ∣ Dom α ∣, the collapse of α is c(α) = ∣ ∪t∈Imα{tα⁻¹ :∣ tα⁻¹ ∣≥ 2} ∣, fix of α is f(α) = ∣ {x ∈ Xn : xα = x} ∣, the height of α is ∣ Imα ∣, and the rig...
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| Дата: | 2014 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2014
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152350 |
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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 partial transformation semigroups / A. Umar // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 1. — С. 110–134. — Бібліогр.: 56 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1523502019-06-11T01:25:17Z Some combinatorial problems in the theory of partial transformation semigroups Umar, A. Let Xn = {1,2,…,n}. On a partial transformation α : Dom α ⊆ Xn → Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is ∣ Dom α ∣, the collapse of α is c(α) = ∣ ∪t∈Imα{tα⁻¹ :∣ tα⁻¹ ∣≥ 2} ∣, fix of α is f(α) = ∣ {x ∈ Xn : xα = x} ∣, the height of α is ∣ Imα ∣, and the right [left] waist of α is max(Imα) [min(Imα)]. The cardinalities of some equivalences defined by equalities of these parameters on Tn, the semigroup of full transformations of Xn, and Pn the semigroup of partial transformations of Xn and some of their notable subsemigroups that have been computed are gathered together and the open problems highlighted. 2014 Article Some combinatorial problems in the theory of partial transformation semigroups / A. Umar // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 1. — С. 110–134. — Бібліогр.: 56 назв. — англ. 1726-3255 2010 MSC:20M17, 20M20, 05A10, 05A15. http://dspace.nbuv.gov.ua/handle/123456789/152350 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}. On a partial transformation α : Dom α ⊆ Xn → Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is ∣ Dom α ∣, the collapse of α is c(α) = ∣ ∪t∈Imα{tα⁻¹ :∣ tα⁻¹ ∣≥ 2} ∣, fix of α is f(α) = ∣ {x ∈ Xn : xα = x} ∣, the height of α is ∣ Imα ∣, and the right [left] waist of α is max(Imα) [min(Imα)]. The cardinalities of some equivalences defined by equalities of these parameters on Tn, the semigroup of full transformations of Xn, and Pn the semigroup of partial transformations of Xn and some of their 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 partial transformation semigroups Algebra and Discrete Mathematics |
| author_facet |
Umar, A. |
| author_sort |
Umar, A. |
| title |
Some combinatorial problems in the theory of partial transformation semigroups |
| title_short |
Some combinatorial problems in the theory of partial transformation semigroups |
| title_full |
Some combinatorial problems in the theory of partial transformation semigroups |
| title_fullStr |
Some combinatorial problems in the theory of partial transformation semigroups |
| title_full_unstemmed |
Some combinatorial problems in the theory of partial transformation semigroups |
| title_sort |
some combinatorial problems in the theory of partial transformation semigroups |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152350 |
| citation_txt |
Some combinatorial problems in the theory of partial transformation semigroups / A. Umar // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 1. — С. 110–134. — Бібліогр.: 56 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT umara somecombinatorialproblemsinthetheoryofpartialtransformationsemigroups |
| first_indexed |
2023-05-20T17:38:07Z |
| last_indexed |
2023-05-20T17:38:07Z |
| _version_ |
1796153740581928960 |