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

Victoria Lebed (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Domaines: Combinatoire [math.CO]

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