On factorisations and generators in transformation semigroups.
A cycle-style notation is introduced for members of the full transformation semigroup similar to that used by Lipscomb for partial one-to-one maps. This approach is used to study generating sets of the submonoids \(T_{n,r}\) of \(T_n\) consisting of the union of the symmetric group and the ideal of all mappings with range of cardinality no greater than \(r\) (\(\leq n\)). The least number of singular elements in any generating set for \(T_{n,r}\) is the number of partitions of \(n\) with \(r\) terms.
scientific article; zbMATH DE number 2173797