On monotone alternating inverse monoids

VÃ­tor Hugo Fernandes

algebra

On monotone alternating inverse monoids

arXiv:2503.00820

summary

The paper investigates two inverse submonoids of the alternating inverse monoid on a finite chain, determining their cardinalities, describing their Green's relations and congruences, and computing their ranks.

Abstract

In this paper, we consider the inverse submonoids $A M_{n}$ of monotone transformations and $A O_{n}$ of order-preserving transformations of the alternating inverse monoid $A I_{n}$ 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 $A I_{n}$ .

Topics & keywords

#inverse monoids #monotone transformations #order-preserving transformations #Green's relations #congruencesalternating inverse monoidAM_nAO_ncardinalityrank