Chinese monoid

From Wikipedia, the free encyclopedia
Jump to: navigation, search

In mathematics, the Chinese monoid is a monoid generated by a totally ordered alphabet with the relations cba = cab = bca for every abc. An algorithm similar to Schensted's algorithm yields characterisation of the equivalence classes and a cross-section theorem. It was discovered by Duchamp & Krob (1994) during their classification of monoids with growth similar to that of the plactic monoid, and studied in detail by Julien Cassaigne, Marc Espie, Daniel Krob, Jean-Christophe Novelli, and Florent Hivert in 2001.[1]

The Chinese monoid has a regular language cross-section

and hence polynomial growth of dimension .[2]


  1. ^ Cassaigne, Julien; Espie, Marc; Krob, Daniel; Novelli, Jean-Christophe; Hivert, Florent (2001), "The Chinese monoid", International Journal of Algebra and Computation, 11 (3): 301–334, ISSN 0218-1967, MR 1847182, Zbl 1024.20046, doi:10.1142/S0218196701000425 
  2. ^ Jaszuńska, Joanna; Okniński, Jan (2011), "Structure of Chinese algebras.", J. Algebra, 346 (1): 31–81, ISSN 0021-8693, Zbl 1246.16022, arXiv:1009.5847Freely accessible, doi:10.1016/j.jalgebra.2011.08.020