Obtaining the poset of the Catalan monoid
The poset Pn is defined as the poset consisting of subsets of { 1,...,n } where for two subsets X≤Y if and only if X and Y have the same cardinality and if X= {x_1 < ... < x_k } and Y= {y_1 < ... < y_k } we have xi≤yi for i=1,...,k. See for example https://arxiv.org/pdf/1806.06531.pdf .
My question is whether the is an easy way to obtain this poset for a given n with Sage?