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

Cain, Alan J., Gray, Robert and Malheiro, António (2015) Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids. International Journal of Algebra and Computation, 25 (01n02). ISSN 0218-1967

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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.

Item Type: Article
Uncontrolled Keywords: chinese monoid,hypoplactic monoid,sylvester monoid,finite complete rewriting systems,automaticity,biautomaticity
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Pure Connector
Date Deposited: 24 Jul 2015 21:29
Last Modified: 22 Jul 2020 00:09
URI: https://ueaeprints.uea.ac.uk/id/eprint/53528
DOI: 10.1142/S0218196715400044

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