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)...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2010 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2010
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154602 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862544290846081024 |
|---|---|
| author | Umar, A. |
| author_facet | Umar, A. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-11-25T01:53:17Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154602 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-25T01:53:17Z |
| publishDate | 2010 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Umar, A. 2019-06-15T16:43:30Z 2019-06-15T16:43:30Z 2010 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 https://nasplib.isofts.kiev.ua/handle/123456789/154602 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. The ideas for this work were formed during a one month stay at Wilfrid LaurierUniversity in the Summer of 2007.2This paper is based on the talk I gave at the 22nd BCC Conference, University ofSt Andrews, July 2009. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Some combinatorial problems in the theory of symmetric inverse semigroups Article published earlier |
| spellingShingle | Some combinatorial problems in the theory of symmetric inverse semigroups Umar, A. |
| title | 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_short | Some combinatorial problems in the theory of symmetric inverse semigroups |
| title_sort | some combinatorial problems in the theory of symmetric inverse semigroups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154602 |
| work_keys_str_mv | AT umara somecombinatorialproblemsinthetheoryofsymmetricinversesemigroups |