  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.
