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
Автор: Umar, A.
Формат: Стаття
Мова:English
Опубліковано: Інститут прикладної математики і механіки НАН України 2010
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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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
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