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

^ 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
^ 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

Duchamp, Gérard; Krob, Daniel (1994), "Plactic-growth-like monoids", Words, languages and combinatorics, II (Kyoto, 1992), World Sci. Publ., River Edge, NJ, pp. 124–142, MR 1351284, Zbl 0875.68720

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[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

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