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      Hook, line and sinker: a bijective proof of the skew shifted hook-length formula

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          Abstract

          A few years ago, Naruse presented a beautiful cancellation-free hook-length formula for skew shapes, both straight and shifted. The formula involves a sum over objects called \emph{excited diagrams}, and the term corresponding to each excited diagram has hook lengths in the denominator, like the classical hook-length formula due to Frame, Robinson and Thrall. Recently, the formula for skew straight shapes was proved via a simple bumping algorithm. The aim of this paper is to extend this result to skew shifted shapes. Since straight skew shapes are special cases of skew shifted shapes, this is a bijection that proves the whole family of hook-length formulas, and is also the simplest known bijective proof for shifted (non-skew) shapes. A weighted generalization of Naruse's formula is also presented.

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          Excited Young diagrams and equivariant Schubert calculus

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            Another Involution Principle-Free Bijective Proof of Stanley's Hook-Content Formula

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              On selecting a random shifted young tableau

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                Author and article information

                Journal
                07 September 2018
                Article
                1809.02389
                c943b0ea-49c2-4567-b550-157c0351f53f

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                math.CO

                Combinatorics
                Combinatorics

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