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 \(\mathbf{HK}_\Gamma\) associated with a simple oriented graph \(\Gamma\). We use confluence properties from [7] to associate with each...
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| Дата: | 2021 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2021
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1571 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543239318798336 |
|---|---|
| author | Aragona, R. D'Andrea, A. |
| author_facet | Aragona, R. D'Andrea, A. |
| author_sort | Aragona, R. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2021-01-29T09:38:49Z |
| 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 \(\mathbf{HK}_\Gamma\) associated with a simple oriented graph \(\Gamma\). We use confluence properties from [7] to associate with each element in \(\mathbf{HK}_\Gamma\) 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. |
| first_indexed | 2025-12-02T15:30:23Z |
| format | Article |
| id | admjournalluguniveduua-article-1571 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:30:23Z |
| publishDate | 2021 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-15712021-01-29T09:38:49Z Normal form in Hecke-Kiselman monoids associated with simple oriented graphs Aragona, R. D'Andrea, A. simple oriented graph, Hecke-Kiselman monoid, normal form 20M05, 20M10 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 \(\mathbf{HK}_\Gamma\) associated with a simple oriented graph \(\Gamma\). We use confluence properties from [7] to associate with each element in \(\mathbf{HK}_\Gamma\) 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. Lugansk National Taras Shevchenko University Alessandro D'Andrea was partially supported by Ateneo fundings from Sapienza University in Rome. 2021-01-29 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1571 10.12958/adm1571 Algebra and Discrete Mathematics; Vol 30, No 2 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1571/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1571/686 Copyright (c) 2021 Algebra and Discrete Mathematics |
| spellingShingle | simple oriented graph Hecke-Kiselman monoid normal form 20M05 20M10 Aragona, R. D'Andrea, A. Normal form in Hecke-Kiselman monoids associated with simple oriented graphs |
| 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 |
| topic | simple oriented graph Hecke-Kiselman monoid normal form 20M05 20M10 |
| topic_facet | simple oriented graph Hecke-Kiselman monoid normal form 20M05 20M10 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1571 |
| work_keys_str_mv | AT aragonar normalforminheckekiselmanmonoidsassociatedwithsimpleorientedgraphs AT dandreaa normalforminheckekiselmanmonoidsassociatedwithsimpleorientedgraphs |