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 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.
The Chinese monoid has a regular language cross-section
and hence polynomial growth of dimension formula_2.
The Chinese monoid equivalence class of a permutation is the preimage of an involution under the map formula_3 where formula_4 denotes the product in the Iwahori-Hecke algebra with formula_5.