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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.

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