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Sierpiński 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 Ruškuc stating that every such countable set of partial bijections may be obtained as the composition of two partial bijections and their inverses.

preprint2012arXivOpen access
James T. HydeYann Péresse
math.GRmath.RA
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James T. HydeYann Péresse

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