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Abstract: We introduce a shifted analog of the plactic monoid of Lascoux andSch\-utzenberger, the \emph{shifted plactic monoid}. It can be defined in twodifferent ways: via the \emph{shifted Knuth relations}, or using Haiman-s mixedinsertion.Applications include: a new combinatorial derivation and a new version ofthe shifted Littlewood-Richardson Rule; similar results for the coefficients inthe Schur expansion of a Schur $P$-function; a shifted counterpart of theLascoux-Sch\-utzenberger theory of noncommutative Schur functions in placticvariables; a characterization of shifted tableau words; and more.

Author: Luis Serrano



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