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On the hypoplactic monoid. (English) Zbl 0960.05106
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
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