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

Alan J. Cain, Robert Gray, António Malheiro

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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
Article number51
JournalInternational Journal of Algebra and Computation
Volume25
Issue number01n02
DOIs
Publication statusPublished - 3 Feb 2015

Keywords

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

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