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Abstract for  C. Krattenthaler,  Bijective proofs of the hook formulas
for the number of standard Young tableaux, ordinary and shifted

Bijective proofs of the hook formulas for the number of ordinary
standard Young tableaux and for the number of shifted standard Young
tableaux are given. They are formulated in a uniform manner, and in
fact prove $q$-analogues of the ordinary and shifted hook formulas.
The proofs proceed by combining the ordinary, respectively shifted,
Hillman--Grassl algorithm and Stanley's $(P,\omega)$-partition theorem
with the involution principle of Garsia and Milne.

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