Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids

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Abstract

This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoids, hypoplactic monoids, and sylvester monoids. For Chinese monoids, we first give new presentations via finite complete rewriting systems, using more lucid constructions and proofs than those given independently by Chen & Qui and Güzel Karpuz; we then construct biautomatic structures. For hypoplactic monoids, we construct finite complete rewriting systems and biautomatic structures. For sylvester monoids, which are not finitely presented, we prove that the standard presentation is an infinite complete rewriting system, and construct biautomatic structures. Consequently, the monoid algebras corresponding to monoids of these classes are automaton algebras in the sense of Ufnarovskij.

Original languageEnglish
Pages (from-to)51-80
Number of pages30
JournalInternational Journal Of Algebra And Computation
Volume25
Issue number1-2
DOIs
Publication statusPublished - 25 Apr 2015
EventInternational Conference on Geometric, Combinatorial, and Dynamics Aspects of Semigroup Theory and Group Theory - Bar Ilan University, Ramat Gan, Israel
Duration: 11 Jun 201314 Jun 2013

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Keywords

  • automaticity
  • biautomaticity
  • Chinese monoid
  • finite complete rewriting systems
  • hypoplactic monoid
  • sylvester monoid

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