##### This material has been published in
Electronic
J. Combin. **2** (1995), #R13, 9 pp.

## Christian Krattenthaler

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

### (9 pages)

**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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