Asymptotic Results for Semigroups of Order-Preserving Partial Transformations
Abdallah Laradji, Abdullahi Umar ยท Communications in Algebra ยท 2006
Let ๐ซ ๎ข n be the semigroup of all decreasing and order-preserving partial transformations of an n-element chain, and let E(๐ซ ๎ข n ) be its set of idempotents. Among other results, asymptotic formulae for |๐ซ ๎ข n | and |E(๐ซ ๎ข n )|/|๐ซ ๎ข n | are obtained. Similar results for ๐ซ ๎ฎ n the (larger) semigroup of all order-preserving partial transformations of an n-element chain are also obtained.