Normal form in Hecke-Kiselman monoids associated with simple oriented graphs
Combinatorics
2022-05-25 v1
Abstract
We generalize Kudryavtseva and Mazorchuk's concept of canonical form of elements in Kiselman's semigroups to the setting of a Hecke-Kiselman monoid associated with a simple oriented graph . We use confluence properties to associate with each element in 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.
Cite
@article{arxiv.1904.10745,
title = {Normal form in Hecke-Kiselman monoids associated with simple oriented graphs},
author = {Riccardo Aragona and Alessandro D'Andrea},
journal= {arXiv preprint arXiv:1904.10745},
year = {2022}
}