Combinatorial aspects of transformation semigroups
Peter M. Higgins · 1992
Abstract In this section we shall introduce results of a probabilistic nature concerning finite transformation semigroups. The study of random functions has a wide literature of its own, and many questions along these lines lead to occupancy problems which arise throughout mathematics and physics, particularly in mathematical genetics (Kingman 1978). We concentrate here on results that are of interest to semigroupists and which have elementary proofs. Indeed, one justification for the inclusion of this material is the delightful manner in which classic results from analysis and combinatorics furnish answers to a number of natural questions concerningTn andOn (the semigroup of all order-preserving mappings on {l, … , n}).