Sierpi\'nski rank of the Symmetric inverse semigroup
  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 Ru\v{s}kuc stating that every such countable set of partial bijections may be obtained as the composition of two partial bijections and their inverses. 
James T. Hyde, Yann P\'eresse
math.GR math.RA