Bijective proofs of the hook formulas for the number of standard Young tableaux, ordinary and shifted (Q1894658)

Summary: 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.