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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| Мова: | English |
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Lugansk National Taras Shevchenko University
2021
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua: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 |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2021-01-29T09:38:49Z |
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OJS |
| language |
English |
| topic |
simple oriented graph Hecke-Kiselman monoid normal form 20M05 20M10 |
| 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 |
| topic_facet |
simple oriented graph Hecke-Kiselman monoid normal form 20M05 20M10 |
| format |
Article |
| author |
Aragona, R. D'Andrea, A. |
| 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 |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2021 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1571 |
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AT aragonar normalforminheckekiselmanmonoidsassociatedwithsimpleorientedgraphs AT dandreaa normalforminheckekiselmanmonoidsassociatedwithsimpleorientedgraphs |
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2025-07-17T10:32:24Z |
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2025-07-17T10:32:24Z |
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