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<p>In this paper, we consider the inverse submonoids <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {AOR}_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">AOR</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> of oriented transformations and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {AOP}_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">AOP</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> of orientation-preserving transformations of the alternating inverse monoid <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal{A}\mathcal{I}_n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">A</mi> <msub> <mi mathvariant="script">I</mi> <mi>n</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> on a chain with <i>n</i> elements. We compute the cardinalities, describe the Green’s structures and the congruences, and calculate the ranks of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {AOR}_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">AOR</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathcal {AOP}_n.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">AOP</mi> <mi>n</mi> </msub> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation></p>

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On oriented alternating inverse monoids

  • 期刊论文

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  • 发表日期：

    2026年2月27日

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  • Vítor Hugo Fernandes

摘要

In this paper, we consider the inverse submonoids \(\mathcal {AOR}_n\) AOR n of oriented transformations and \(\mathcal {AOP}_n\) AOP n of orientation-preserving transformations of the alternating inverse monoid \(\mathcal{A}\mathcal{I}_n\) 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 \(\mathcal {AOR}_n\) AOR n and \(\mathcal {AOP}_n.\) AOP n .