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Zbl 1024.20046
Cassaigne, Julien; Espie, Marc; Krob, Daniel; Novelli, Jean-Christophe; Hivert, Florent
The Chinese monoid. (English)
[J] Int. J. Algebra Comput. 11, No. 3, 301-334 (2001). ISSN 0218-1967

Summary: This paper presents a combinatorial study of the Chinese monoid, a ternary monoid related to the plactic monoid and based on the relation scheme $cba\equiv bca\equiv cab$. An algorithm similar to Schensted's algorithm yields a characterization of the equivalence classes and a cross-section theorem. We also establish a Robinson-Schensted correspondence for the Chinese monoid before computing the order of specific Chinese classes. For this work, we had to develop some new combinatorial tools. Among other things we discovered an embedding of every equivalence class in the largest one. Finally, the end of this paper is devoted to the study of conjugacy classes.

MSC 2000:: *20M05 Free semigroups
05E10 Tableaux, etc.
68R15 Combinatorics on words

Keywords: Chinese monoid; plactic monoid; algorithms

Cited in: Zbl 1165.16013

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