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February 28, 2026Periodica Mathematica Hungarica0 citationsOpen Access

On oriented alternating inverse monoids

VFVítor Hugo Fernandes

Key Points

  • The aim is to explore the properties and structures of oriented inverse monoids and their cardinalities.
  • Computed the cardinalities of the submonoids \( \mathcal{AOR}_n \) and \( \mathcal{AOP}_n \)
  • Described the Green’s structures associated with these monoids
  • Analyzed the congruences related to \( \mathcal{AOR}_n \) and \( \mathcal{AOP}_n \)
  • Calculated the ranks of \( \mathcal{AOR}_n \) and \( \mathcal{AOP}_n \)
  • The cardinalities for \( \mathcal{AOR}_n \) and \( \mathcal{AOP}_n \) were determined explicitly.
  • Green's structures revealed interesting properties of these transformations.
  • Congruences displayed specific traits unique to oriented transformations.
  • Ranks provided insights into the algebraic complexity of the studied monoids.

Abstract

Abstract In this paper, we consider the inverse submonoids AORₙ AOR n of oriented transformations and AOPₙ AOP n of orientation-preserving transformations of the alternating inverse monoid AIₙ 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 AORₙ AOR n and AOPₙ. AOP n.

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Cite This Study

Vítor Hugo Fernandes (2026) studied this question.

synapsesocial.com/papers/69a287e20a974eb0d3c03c16https://doi.org/10.1007/s10998-026-00702-3
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