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arXiv · 2407.05084

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

Vítor H. Fernandes
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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.

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Vítor H. Fernandes. 2024-07-06. On the monoid of order-preserving transformations of a finite chain whose ranges are intervals. https://arxiv.org/abs/2407.05084

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