Normal form in Hecke-Kiselman monoids associated with simple oriented graphs

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 ${\mathbf{HK}}_{\Gamma }$ associated with a simple oriented graph $\Gamma$. We use confluence properties 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.

References in corpus (1)

• Hecke-Kiselman Monoids of Small Cardinality