Department of Mathematical Sciences , KFUPM , Dhahran, Saudi Arabia
Abstract:
Let 𝒫n be the semigroup of all decreasing and order-preserving partial transformations of an n-element chain, and let E(𝒫n) be its set of idempotents. Among other results, asymptotic formulae for |𝒫n| and |E(𝒫n)|/|𝒫n| are obtained. Similar results for 𝒫n the (larger) semigroup of all order-preserving partial transformations of an n-element chain are also obtained.