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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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.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| _version_ | 1862734765040336896 |
|---|---|
| author | Aragona, R. D'Andrea, A. |
| author_facet | Aragona, R. D'Andrea, A. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T19:44:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188560 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:44:19Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Aragona, R. D'Andrea, A. 2023-03-06T14:18:55Z 2023-03-06T14:18:55Z 2020 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 https://nasplib.isofts.kiev.ua/handle/123456789/188560 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. Both authors are members of INdAM-GNSAGA. The second named author was partially supported by Ateneo fundings from Sapienza University in Rome en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Normal form in Hecke-Kiselman monoids associated with simple oriented graphs Article published earlier |
| spellingShingle | Normal form in Hecke-Kiselman monoids associated with simple oriented graphs Aragona, R. D'Andrea, A. |
| title | 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_short | Normal form in Hecke-Kiselman monoids associated with simple oriented graphs |
| title_sort | normal form in hecke-kiselman monoids associated with simple oriented graphs |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188560 |
| work_keys_str_mv | AT aragonar normalforminheckekiselmanmonoidsassociatedwithsimpleorientedgraphs AT dandreaa normalforminheckekiselmanmonoidsassociatedwithsimpleorientedgraphs |