<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Fernandes, Vítor H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On monotone alternating inverse monoids</style></title></titles><dates><year><style  face="normal" font="default" size="100%">Submitted</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2503.00820</style></url></web-urls></urls><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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.&lt;/p&gt;
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