English

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

Combinatorics 2021-02-18 v1

Abstract

We exhibit explicit and easily realisable bijections between Hecke--Kiselman monoids of type AnA_n/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.

Keywords

Cite

@article{arxiv.2102.08647,
  title  = {The word problem for Hecke--Kiselman monoids of type $A_n$ and $\widetilde{A}_n$},
  author = {Victoria Lebed},
  journal= {arXiv preprint arXiv:2102.08647},
  year   = {2021}
}