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) 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
- [math]\displaystyle{ a^* \ (ba)^*b^* \ (ca)^*(cb)^* c^* \cdots }[/math]
and hence polynomial growth of dimension [math]\displaystyle{ \frac{n(n+1)}{2} }[/math].[2]
The Chinese monoid equivalence class of a permutation is the preimage of an involution under the map [math]\displaystyle{ w \mapsto w \circ w^{-1} }[/math] where [math]\displaystyle{ \circ }[/math] denotes the product in the Iwahori-Hecke algebra with [math]\displaystyle{ q_s = 0 }[/math].[3]
See also
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, http://www.worldscinet.com/ijac/11/1103/S0218196701000425.html
- ↑ Jaszuńska, Joanna; Okniński, Jan (2011), "Structure of Chinese algebras.", J. Algebra 346 (1): 31–81, doi:10.1016/j.jalgebra.2011.08.020, ISSN 0021-8693
- ↑ Hamaker, Zachary; Marberg, Eric; Pawlowski, Brendan (2017-05-01). "Involution words II: braid relations and atomic structures" (in en). Journal of Algebraic Combinatorics 45 (3): 701–743. doi:10.1007/s10801-016-0722-6. ISSN 1572-9192. https://doi.org/10.1007/s10801-016-0722-6.
- 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, http://www.liafa.jussieu.fr/web9/rapportrech/description_en.php?idrapportrech=487
 |  |
