Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ORIENTED TRANSFORMATIONS ON A FINITE CHAIN: ANOTHER DESCRIPTION

  • Vitor H. Fernandes (Center for Mathematics and Applications (NovaMath) and Department of Mathematics Faculdade de Ciencias e Tecnologia Universidade Nova de Lisboa)
  • Received : 2022.09.10
  • Accepted : 2022.11.25
  • Published : 2023.07.31
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Abstract

Following the new description of an oriented full transformation on a finite chain given recently by Higgins and Vernitski in [4], in this short note we present a refinement of this description which is extendable to partial transformations and to injective partial transformations.

Keywords

Acknowledgement

This work is funded by national funds through the FCT - Fundacao para a Ciencia e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (NovaMath - Center for Mathematics and Applications).

References

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  2. V. H. Fernandes, The monoid of all injective orientation preserving partial transformations on a finite chain, Comm. Algebra 28 (2000), no. 7, 3401-3426. https://doi.org/10.1080/00927870008827033
  3. V. H. Fernandes and T. Paulista, On the monoid of partial isometries of a cycle graph, arXiv:2205.02196v2 (2022).
  4. P. M. Higgins and A. Vernitski, Orientation-preserving and orientation-reversing mappings: a new description, Semigroup Forum 104 (2022), no. 2, 509-514. https://doi.org/10.1007/s00233-022-10256-8
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