Sierpiński rank of the Symmetric inverse semigroup
arXiv:1211.6284
Abstract
We show that every countable set of partial bijections from an infinite set to itself can be obtained as a composition of just two such partial bijections. This strengthens a result by Higgins, Howie, Mitchell and Ruškuc stating that every such countable set of partial bijections may be obtained as the composition of two partial bijections and their inverses.