Combinatorial results for semigroups of order-decreasing partial transformations
J. Integer Seq. 7(3), Art. 04.3.8, 14 p., electronic only (2004)
Summary
Summary: Let $PC_{n}$ be the semigroup of all decreasing and order-preserving partial transformations of a finite chain. It is shown that |$PC_{n}| = r_{n}$, where $r_{n}$ is the large (or double) Schröder number. Moreover, the total number of idempotents of $PC_{n}$ is shown to be $(3^{n}+1)/2$.
