Chinese monoid

In mathematics, the Chinese monoid is a monoid generated by a totally ordered alphabet with the relations cba = cab = bca for every a ≤ b ≤ c. 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

a^* \ (ba)^*b^* \ (ca)^*(cb)^* c^* \cdots \

and hence polynomial growth of dimension \frac{n(n+1)}{2}.[2]

References

  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, doi:10.1142/S0218196701000425, ISSN 0218-1967, MR 1847182, Zbl 1024.20046
  2. ↑ Jaszuńska, Joanna; Okniński, Jan (2011), "Structure of Chinese algebras.", J. Algebra 346 (1): 31–81, arXiv:1009.5847, doi:10.1016/j.jalgebra.2011.08.020, ISSN 0021-8693, Zbl 1246.16022