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

Abstract

We exhibit explicit and easily realisable bijections between Hecke--Kiselman monoids of type $A_n$/${\tilde{A}}_n$; 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.

References in corpus (1)

• On Kiselman quotients of 0-Hecke monoids