Английская Википедия: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 Шаблон:Harvtxt 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> a^* \ (ba)^*b^* \ (ca)^*(cb)^* c^* \cdots </math>
and hence polynomial growth of dimension <math>\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>w \mapsto w \circ w^{-1}</math> where <math>\circ</math> denotes the product in the Iwahori-Hecke algebra with <math>q_s = 0</math>.[3]
See also
References
Шаблон:Combin-stub
Шаблон:Abstract-algebra-stub
