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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2020 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/188560 |
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| Zitieren: | 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. |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Normal form in Hecke-Kiselman monoids associated with simple oriented graphs |
| spellingShingle |
Normal form in Hecke-Kiselman monoids associated with simple oriented graphs Aragona, R. D'Andrea, A. |
| 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 |
| author |
Aragona, R. D'Andrea, A. |
| author_facet |
Aragona, R. D'Andrea, A. |
| publishDate |
2020 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT aragonar normalforminheckekiselmanmonoidsassociatedwithsimpleorientedgraphs AT dandreaa normalforminheckekiselmanmonoidsassociatedwithsimpleorientedgraphs |
| first_indexed |
2025-12-07T19:44:19Z |
| last_indexed |
2025-12-07T19:44:19Z |
| _version_ |
1850879937604485120 |