The word problem for Hecke--Kiselman monoids of type A_n and \widetildeA_n

2021/02/17 by Victoria Lebed, Lebed, Victoria · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2102.08647

openalex publication_date 2021/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• A complete classification of endomorphisms of Kiselman's semigroup

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• The Word Problem for the Singular Braid Monoid
• Reduce Problems From Braid Groups To Braid Monoids
• Explicit Presentations for the Dual Braid Monoids
• Effective representations of Hecke-Kiselman monoids of type A
• The Finite Basis Problem for Kiselman Monoids