Confluence of the Chinese Monoid

  • Jörg EndrullisEmail author
  • Jan Willem Klop
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11760)


The Chinese monoid, related to Knuth’s Plactic monoid, is of great interest in algebraic combinatorics. Both are ternary monoids, generated by relations between words of three symbols. The relations are, for a totally ordered alphabet, \(cba = cab = bca\) if \(a \le b \le c\). In this note we establish confluence by tiling for the Chinese monoid, with the consequence that every two words uv have extensions to a common word: \(\forall u, v. \;\exists x, y. \;ux = vy\).

Our proof is given using decreasing diagrams, a method for obtaining confluence that is central in abstract rewriting theory. Decreasing diagrams may also be applicable to various related monoid presentations.

We conclude with some open questions for the monoids considered.


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Authors and Affiliations

  1. 1.Vrije Universiteit AmsterdamAmsterdamThe Netherlands
  2. 2.Centrum Wiskunde en InformaticaAmserdamThe Netherlands

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