Another Involution Principle-Free Bijective Proof of Stanley's Hook-Content Formula

Another bijective proof of Stanley’s hook-content formula for the generating function for semistandard tableaux of a given shape is given that does not 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 bijective proof (“An involution principle-free bijective proof of Stanley’s hook-content formula”, Discrete Math. Theoret. Computer Science, to appear) and the Novelli-Pak-Stoyanovskii bijection (Discrete Math. Theoret. Computer Science 1 (1997), 53–67) for the hook formula for standard Young tableaux of a given shape. This new algorithm can also be used as an algorithm for the random generation of tableaux of a given shape with bounded entries. An appropriate deformation of this algorithm gives an algorithm for the random generation of plane partitions inside a given box.