On the monoid of order-preserving transformations of a finite chain whose ranges are intervals

Vítor H. Fernandes

On the monoid of order-preserving transformations of a finite chain whose ranges are intervals

Rings and Algebras 2024-07-09 v1

Authors: Vítor H. Fernandes

Abstract

In this note we give a presentation for the monoid $IO_n$ of all order-preserving transformations of a $n$ -chain whose ranges are intervals. We also consider the submonoid $IO_n^-$ of $IO_n$ consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.

Keywords

order-preserving transformations finite chain intervals monoid presentation rank order-decreasing transformations

Cite

@article{arxiv.2407.05084,
  title  = {On the monoid of order-preserving transformations of a finite chain whose ranges are intervals},
  author = {Vítor H. Fernandes},
  journal= {arXiv preprint arXiv:2407.05084},
  year   = {2024}
}

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