Séminaire Lotharingien de Combinatoire, 80B.13 (2018), 12 pp.
Matjaž Konvalinka
A Bijective Proof of the Hook-Length Formula for Skew Shapes
Abstract.
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.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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