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arXiv · 1904.10745

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

Riccardo Aragona·Alessandro D'Andrea
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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.

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Riccardo Aragona, Alessandro D'Andrea. 2019-04-24. Normal form in Hecke-Kiselman monoids associated with simple oriented graphs. https://doi.org/10.12958/adm1571

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