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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| Date: | 2021 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2021
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1571 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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. |
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