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The Chinese monoid. (English) Zbl 1024.20046
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 cbabcacab. 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:
20M05Free semigroups, generators and relations, word problems
05E10Combinatorial aspects of representation theory
68R15Combinatorics on words