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{\bf Matja\v z Konvalinka}
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{\bf The Weighted Hook Length Formula III: Shifted Tableaux}
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Recently, a simple proof of the hook length formula was given via the
branching rule. In this paper, we extend the results to shifted
tableaux. We give a bijective proof of the branching rule for the hook
lengths for shifted tableaux; present variants of this rule, including
weighted versions; and make the first tentative steps toward a
bijective proof of the hook length formula for $d$-complete posets.

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