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<p>We exhibit explicit and easily realisable bijections between Hecke–Kiselman monoids of type <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="233_2025_10543_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(A_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>/<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="233_2025_10543_Article_IEq2.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(\widetilde{A}_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mi>A</mi> <mo stretchy="true">~</mo> </mover> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>; certain braid diagrams on the plane/cylinder; and couples of integer sequences of particular types. This yields a fast solution of the word problem and an efficient normal form for these HK monoids. Yang–Baxter type actions play an important role in our constructions.</p>

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The word problem for Hecke–Kiselman monoids of type \(A_n\) and \(\widetilde{A}_n\)

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Victoria Lebed

摘要

We exhibit explicit and easily realisable bijections between Hecke–Kiselman monoids of type \(A_n\) A n / \(\widetilde{A}_n\) A ~ n ; certain braid diagrams on the plane/cylinder; and couples of integer sequences of particular types. This yields a fast solution of the word problem and an efficient normal form for these HK monoids. Yang–Baxter type actions play an important role in our constructions.