On the hypoplactic monoid. (English) Zbl 0960.05106

Novelli, Jean-Christophe

Discrete Math. 217, No. 1-3, 315-336 (2000).

Summary: This paper presents a combinatorial study of the hypoplactic monoid that is the analogue of the plactic monoid in the theory of noncommutative symmetric functions. After having recalled its definition using rewritings, we provide a new definition and use this one to prove combinatorially that each hypoplactic class contains exactly one quasi-ribbon word. We then prove hypoplactic analogues of classical results of the plactic monoid and, in particular, we study the analogues of Schur functions.

MSC:

05E05	Symmetric functions and generalizations
05E10	Combinatorial aspects of representation theory
20M99	Semigroups

Keywords:

hypoplactic monoid; noncommutative symmetric functions; quasi-ribbon word; Schur functions