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Ranks and presentations of some normally ordered inverse semigroups

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Abstract

In this paper we compute the rank and exhibit a presentation for the monoids of all P-stable and P-order preserving partial permutations on a finite set \(\Omega \), with P an ordered uniform partition of \(\Omega \). These (inverse) semigroups constitute a natural class of generators of the pseudovariety of inverse semigroups \(\mathsf{NO}\) of all normally ordered (finite) inverse semigroups.

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Acknowledgements

We acknowledge the anonymous referee for the valuable suggestions. We wish to express to him/her our thanks.

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Authors and Affiliations

  1. Departamento de Matemática,Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516, Caparica, Monte da Caparica, Portugal

    Rita Caneco & Vítor H. Fernandes

  2. Centro de Matemática e Aplicações, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516, Caparica, Monte da Caparica, Portugal

    Vítor H. Fernandes & Teresa M. Quinteiro

  3. Departamento de Matemática, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emìdio Navarro 1, 1950-062, Lisboa, Portugal

    Teresa M. Quinteiro

Authors
  1. Rita Caneco
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  2. Vítor H. Fernandes
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  3. Teresa M. Quinteiro
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Correspondence to Teresa M. Quinteiro.

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Vítor H. Fernandes: This work is funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P., under the scope of the project UIDB/00297/2020 (Center for Mathematics and Applications).

Teresa M. Quinteiro: This work is funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P., under the scope of the project UIDB/00297/2020 (Center for Mathematics and Applications), and of Área Departamental Matemática do Instituto Superior de Engenharia de Lisboa.

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Caneco, R., Fernandes, V.H. & Quinteiro, T.M. Ranks and presentations of some normally ordered inverse semigroups. Period Math Hung 85, 435–447 (2022). https://doi.org/10.1007/s10998-022-00448-8

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