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Presentations for monoids of finite partial isometries

Semigroup Forum volume 93, pages 97–110 (2016)Cite this article

Abstract

In this paper we give presentations for the monoid \({\mathcal {DP}}_n\) of all partial isometries on \(\{1,\ldots ,n\}\) and for its submonoid \({\mathcal {ODP}}_n\) of all order-preserving partial isometries.

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Acknowledgments

V. H. Fernandes: This work was developed within the FCT Project PEst-OE/MAT/UI0143/2014 of CAUL, FCUL, and of Departamento de Matemática da Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa. T. M. Quinteiro: This work was developed within the FCT Project PEst-OE/MAT/UI0143/2014 of CAUL, FCUL, and of Instituto Superior de Engenharia de Lisboa.

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Authors and Affiliations

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

    Vítor H. Fernandes

  2. Centro de Álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    Vítor H. Fernandes & Teresa M. Quinteiro

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

    Teresa M. Quinteiro

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

Additional information

Communicated by Jorge Almeida.

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Fernandes, V.H., Quinteiro, T.M. Presentations for monoids of finite partial isometries. Semigroup Forum 93, 97–110 (2016). https://doi.org/10.1007/s00233-015-9759-4

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  • DOI: https://doi.org/10.1007/s00233-015-9759-4

Keywords

  • Presentations
  • Transformations
  • Order-preserving
  • Partial isometries