Another involution principle-free bijective proof of Stanley's hook-content formula

Another bijective proof of Stanley's hook-content formula for the generatin g function for semistandard tableaux of a given shape is given that does no t involve the involution principle of Garsia and Milne. It is the result of a merge of the modified jeu de taquin idea from the author's previous bije ctive proof (1998, Discrete Math. Theoret. Comput. Sci. 3, 011-032) and the Novelli-Pak-Stoyanovskii bijection (J. C. Novelli et al., 1997, Discrete M ath. Theoret. Comput. Sei. 1, 53-67) for the hook formula for standard Youn g tableaux of a given shape. This new algorithm can also be used as an algo rithm for the random generation of tableaux of a given shape with bounded e ntries. An appropriate deformation of this algorithm gives an algorithm for the random generation of plane partitions inside a given box. (C) 1999 Aca demic Press.