Normal form in Hecke-Kiselman monoids associated with simple oriented graphs
We generalize Kudryavtseva and Mazorchuk’s concept of a canonical form of elements [9] in Kiselman’s semigroups to the setting of a Hecke-Kiselman monoid HKГ associated with a simple oriented graph Г. We use confluence properties from [7] to associate with each element in HKГ a normal form; normal f...
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| Дата: | 2020 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2020
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/188560 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Normal form in Hecke-Kiselman monoids associated with simple oriented graphs / R. Aragona, A. D'Andrea // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 161–171. — Бібліогр.: 15 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-188560 |
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| record_format |
dspace |
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irk-123456789-1885602023-03-07T01:26:42Z Normal form in Hecke-Kiselman monoids associated with simple oriented graphs Aragona, R. D'Andrea, A. We generalize Kudryavtseva and Mazorchuk’s concept of a canonical form of elements [9] in Kiselman’s semigroups to the setting of a Hecke-Kiselman monoid HKГ associated with a simple oriented graph Г. We use confluence properties from [7] to associate with each element in HKГ a normal form; normal forms are not unique, and we show that they can be obtained from each other by a sequence of elementary commutations. We finally describe a general procedure to recover a (unique) lexicographically minimal normal form. 2020 Article Normal form in Hecke-Kiselman monoids associated with simple oriented graphs / R. Aragona, A. D'Andrea // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 161–171. — Бібліогр.: 15 назв. — англ. 1726-3255 DOI:10.12958/adm1571 2010 MSC: 20M05, 20M10 http://dspace.nbuv.gov.ua/handle/123456789/188560 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 |
We generalize Kudryavtseva and Mazorchuk’s concept of a canonical form of elements [9] in Kiselman’s semigroups to the setting of a Hecke-Kiselman monoid HKГ associated with a simple oriented graph Г. We use confluence properties from [7] to associate with each element in HKГ a normal form; normal forms are not unique, and we show that they can be obtained from each other by a sequence of elementary commutations. We finally describe a general procedure to recover a (unique) lexicographically minimal normal form. |
| format |
Article |
| author |
Aragona, R. D'Andrea, A. |
| spellingShingle |
Aragona, R. D'Andrea, A. Normal form in Hecke-Kiselman monoids associated with simple oriented graphs Algebra and Discrete Mathematics |
| author_facet |
Aragona, R. D'Andrea, A. |
| author_sort |
Aragona, R. |
| title |
Normal form in Hecke-Kiselman monoids associated with simple oriented graphs |
| title_short |
Normal form in Hecke-Kiselman monoids associated with simple oriented graphs |
| title_full |
Normal form in Hecke-Kiselman monoids associated with simple oriented graphs |
| title_fullStr |
Normal form in Hecke-Kiselman monoids associated with simple oriented graphs |
| title_full_unstemmed |
Normal form in Hecke-Kiselman monoids associated with simple oriented graphs |
| title_sort |
normal form in hecke-kiselman monoids associated with simple oriented graphs |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2020 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188560 |
| citation_txt |
Normal form in Hecke-Kiselman monoids associated with simple oriented graphs / R. Aragona, A. D'Andrea // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 161–171. — Бібліогр.: 15 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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AT aragonar normalforminheckekiselmanmonoidsassociatedwithsimpleorientedgraphs AT dandreaa normalforminheckekiselmanmonoidsassociatedwithsimpleorientedgraphs |
| first_indexed |
2023-10-18T23:08:38Z |
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2023-10-18T23:08:38Z |
| _version_ |
1796157361052712960 |