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Paper detail

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

We generalize Kudryavtseva and Mazorchuk's concept of canonical form of elements in Kiselman's semigroups to the setting of a Hecke-Kiselman monoid $\mathbf{HK}_Γ$ associated with a simple oriented graph $Γ$. We use confluence properties to associate with each element in $\mathbf{HK}_Γ$ 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.

preprint2019arXivOpen access
Riccardo AragonaAlessandro D'Andrea
math.CO
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Riccardo AragonaAlessandro D'Andrea

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