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

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

1998-07-13

arxiv.org/abs/math/9807068v1

J. Combin. Theory Ser. A 88 (1999), 66-92

Mathematics

Combinatorics

23 pages, AmS-TeX

Scientific paper

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.

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