This paper computes cardinalities and describes Green's structures in inverse monoids, highlighting key properties.
In this paper, we consider the inverse submonoids AORₙ of oriented transformations and AOPₙ of orientation-preserving transformations of the alternating inverse monoid AIₙ on a chain with n elements. We compute the cardinalities, describe the Green's structures and the congruences, and calculate the ranks of AORₙ and AOPₙ.
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Vítor H. Fernandes (2025) studied this question.
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