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...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2020 |
| ISSN: | 1726-3255 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2020
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188560 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| 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 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.
|
|---|---|
| ISSN: | 1726-3255 |