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Dual equivalence with applications, including a conjecture of Proctor. (English) Zbl 0760.05093
The author establishes a bijection between standard tableaux of “shifted staircase” type and reduced expressions for the longest element in the Coxeter group. He also proves a conjecture of Stanley and determines the “dual Knuth relations” for the shifted Schensted correspondence.

MSC:
05E10 Combinatorial aspects of representation theory
05E05 Symmetric functions and generalizations
20F55 Reflection and Coxeter groups (group-theoretic aspects)
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