A Presentation for the Dual Symmetric Inverse Monoid

The dual symmetric inverse monoid \(\mathscr{I}_n^*\) is the inverse monoid of all isomorphisms between quotients of an \(n\)-set. We give a monoid presentation of \(\mathscr{I}_n^*\) and, along the way, establish criteria for a monoid to be inverse when it is generated by completely regular elements.