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# The word problem for Hecke--Kiselman monoids of type $A_n$ and $\widetilde{A}_n$

Abstract : We exhibit explicit and easily realisable bijections between Hecke--Kiselman monoids of type $A_n$/$\widetilde{A}_n$; 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.
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Preprints, Working Papers, ...
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https://hal-normandie-univ.archives-ouvertes.fr/hal-03142869
Contributor : Victoria Lebed Connect in order to contact the contributor
Submitted on : Tuesday, February 16, 2021 - 1:09:30 PM
Last modification on : Tuesday, October 19, 2021 - 11:33:54 PM
Long-term archiving on: : Monday, May 17, 2021 - 7:09:46 PM

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HK.pdf
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### Identifiers

• HAL Id : hal-03142869, version 1
• ARXIV : 2102.08647

### Citation

Victoria Lebed. The word problem for Hecke--Kiselman monoids of type $A_n$ and $\widetilde{A}_n$. 2021. ⟨hal-03142869⟩

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