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arXiv · 2503.00820

On monotone alternating inverse monoids

Vítor Hugo Fernandes
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Abstract

In this paper, we consider the inverse submonoids $AM_n$ of monotone transformations and $AO_n$ of order-preserving transformations of the alternating inverse monoid $AI_n$ on a chain with $n$ elements. We compute the cardinalities, describe the Green's structures and the congruences, and calculate the ranks of these two submonoids of $AI_n$.

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Vítor Hugo Fernandes. 2025-03-02. On monotone alternating inverse monoids. https://arxiv.org/abs/2503.00820

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