### v2i1r13 — Comment by author, Nov 2, 1998.

An elegant hook bijection (perhaps, THE hook bijection) was found by
Pak and Stoyanovskii [1]. It avoids the involution principle. It works
on the basis of jeu de taquin moves which are recorded in a beautiful
manner. However, [1] does not contain a proof that the algorithm works.
A proof is provided in [2]. Using similar ideas, Novelli and Pak [3] claim
to have found a bijection for the shifted hook formula that avoids the
involution principle.

#### References

[1] I. M. Pak and A. V. Stoyanovskii, A bijective proof of the hook-length
formula and its analogues, Funct. Anal. Appl. 26 (1992), 216-218;
translated from Funkt. Anal. Priloz. 26 (No. 3) (1992), 80-82.

[2] J.-C. Novelli, I. M. Pak and A. V. Stoyanovsii,
A
direct bijective proof of the hook-length formula,
Discrete Math. Theoret. Computer
Science 1 (1997), 53-67.

[3] J.-C. Novelli and I. M. Pak, in preparation.