# Bijective proofs of the hook formulas for the number of standard Young tableaux, ordinary and shifted

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Abstract. 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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