Abstract
It is well-known that the symmetric inverse monoid on a set ofn elements can be generated as a semigroup by its group of units and a single element of rankn − 1. We show that the efficiency with which the semigroup is generated in this way depends solely on the index of nilpotence of the rankn − 1 generator. We also investigate the various ways of expressing elements of the semigroup most efficiently as a product of generators.
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Communicated by J. M. Howie
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Annin, S.A. Hierarchy of efficient generators of the symmetric inverse monoid. Semigroup Forum 54, 327–355 (1997). https://doi.org/10.1007/BF02676615
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DOI: https://doi.org/10.1007/BF02676615