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Mathematics  2007 

A Presentation for the Dual Symmetric Inverse Monoid

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Abstract:

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.

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