Sierpi\'nski rank of the Symmetric inverse semigroup
Group Theory
2012-11-28 v1 Rings and Algebras
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 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.
Keywords
Cite
@article{arxiv.1211.6284,
title = {Sierpi\'nski rank of the Symmetric inverse semigroup},
author = {James T. Hyde and Yann Péresse},
journal= {arXiv preprint arXiv:1211.6284},
year = {2012}
}