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

Comment by the author, November 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.


[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.