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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2014 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152350 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862724500081082368 |
|---|---|
| author | Umar, A. |
| author_facet | Umar, A. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T18:48:09Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-152350 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T18:48:09Z |
| publishDate | 2014 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Umar, A. 2019-06-10T11:03:52Z 2019-06-10T11:03:52Z 2014 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. https://nasplib.isofts.kiev.ua/handle/123456789/152350 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. The ideas for this work were formed during a one month stay at Wilfrid Laurier University in the Summer of 2007. This paper is based on the talk I gave at the 5th NBSAN Meeting, University of St Andrews, May 2010. I would like to thank Professor A. Laradji for his useful suggestions and encouragement. My sincere thanks also to Professor S. Bulman-Fleming and the Department of Mathematics and Statistics, Wilfrid Laurier University. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Some combinatorial problems in the theory of partial transformation semigroups Article published earlier |
| spellingShingle | Some combinatorial problems in the theory of partial transformation semigroups Umar, A. |
| title | 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_short | Some combinatorial problems in the theory of partial transformation semigroups |
| title_sort | some combinatorial problems in the theory of partial transformation semigroups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152350 |
| work_keys_str_mv | AT umara somecombinatorialproblemsinthetheoryofpartialtransformationsemigroups |