Hecke-Kiselman Monoids of Small Cardinality
Abstract
In this paper, we give a characterization of digraphs Q, |Q|≤ 4 such that the associated Hecke-Kiselman monoid HQ is finite. In general, a necessary condition for HQ to be a finite monoid is that Q is acyclic and its Coxeter components are Dynkin diagram. We show, by constructing examples, that such conditions are not sufficient.
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