A Presentation for the Dual Symmetric Inverse Monoid

Abstract

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

21 pp., 6 figures, 2 tables, 7 refs