The algebra of the Catalan monoid as an incidence algebra: A simple proof

Abstract

We give a direct straightforward proof that there is an isomorphism between the algebra of the Catalan monoid C_n that is, the monoid of all order-preserving, weakly increasing self-maps f of [n] = {1,...,n}, over any commutative ring with identity and the incidence algebra of a certain poset over the ring.

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• The word problem for Hecke--Kiselman monoids of type $A_n$ and ${\tilde{A}}_n$
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