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 Cn 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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