Geodesic
A Bijective Proof of the Hook-Length Formula for Skew Shapes
Séminaire lotharingien de combinatoire, 80B (2018)

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Recently, Naruse presented a beautiful cancellation-free hook-length formula for skew shapes. The formula involves a sum over objects called 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.

In this extended abstract, we present a simple bijection that proves an equivalent recursive version of Naruse's result, in the same way that the celebrated hook-walk proof due to Green, Nijenhuis and Wilf gives a bijective (or probabilistic) proof of the hook-length formula for ordinary shapes. In particular, we also give a new bijective proof of the classical hook-length formula, quite different from the known proofs. 

@article{SLC_2018_80B_a12,
     author = {Matja\v{z} Konvalinka},
     title = {A {Bijective} {Proof} of the {Hook-Length} {Formula} for {Skew} {Shapes}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a12/}
}
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AU  - Matjaž Konvalinka
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Matjaž Konvalinka. A Bijective Proof of the Hook-Length Formula for Skew Shapes. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a12/