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Chinese monoid

From Wikipedia, the free encyclopedia

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

and hence polynomial growth of dimension .[2]

The Chinese monoid equivalence class of a permutation is the preimage of an involution under the map where denotes the product in the Iwahori-Hecke algebra with .[3]

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