Combinatorics of nilpotents in symmetric inverse semigroups (Q1881054)

The authors show that several famous combinatorial sequences occur naturally in the context of studying nilpotent elements of the full symmetric inverse semigroup \(I{\mathcal S}_n\). By definition, the semigroup \(I{\mathcal S}_n\) consists of all partial injections from \(\{1,2,\dots,n\}\) to itself. The sequences appear either as the cardinalities of certain nilpotent subsemigroups or as the numbers of special nilpotent elements, and include the Lah numbers, Bell numbers, Stirling numbers of the second kind, Catalan numbers, and binomial coefficients.