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I've noticed that for every natural number $n\in\mathbb{N}$, there is a finite Heyting algebra with cardinality $C(n)$, where $C(n)$ is the $n$th Catalan number, $$1,1,2,5,14,42,132,\ldots$$ I'm ...

Here are some beginner questions on partition algebras... I am trying to understand the monoid called $P_k$ in Tom Halverson, Arun Ram, Partition Algebras. For the sake of simplicity, let $k$ be a ...