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A symmetrical presentation for the singular part of the symmetric inverse monoid

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Abstract

We give a presentation for \({\mathcal{I}_n \ \mathcal{S}_n}\), the semigroup of all singular injective partial transformations on an n-element set, in terms of a particularly symmetrical generating set. Our generators are all restrictions of transpositions, and the relations we obtain display all the symmetry possessed by \({\mathcal{I}_n \ \mathcal{S}_n}\).

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Authors and Affiliations

  1. Centre for Research in Mathematics, School of Computing, Engineering and Mathematics, University of Western Sydney, Locked Bag 1797, Penrith, NSW, 2751, Australia

    James East

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  1. James East
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Correspondence to James East.

Additional information

Presented by M. Jackson.

Dedicated to Brian Davey on the occasion of his 65th birthday

The author would like to express his gratitude to David Easdown for suggesting the problems considered in this work.

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East, J. A symmetrical presentation for the singular part of the symmetric inverse monoid. Algebra Univers. 74, 207–228 (2015). https://doi.org/10.1007/s00012-015-0347-y

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