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      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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          Journal
          0707.2439

          Algebra

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