Hecke-Kiselman monoids of small cardinality.

In this paper, we give a characterization of digraphs Q, | Q|≤4 such that the associated Hecke-Kiselman monoids H are finite. In general, a necessary condition for H to be a finite monoid is that Q is acyclic and its Coxeter components are Dynkin diagrams. We show, by constructing examples, that such conditions are not sufficient. [ABSTRACT FROM AUTHOR]