This material has been published in J. Combin. Theory Ser. A 88 (1999), 66-92, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Academic Press. This material may not be copied or reposted without explicit permission.

Christian Krattenthaler

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

(23 pages)

Abstract. 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 3 (1998), 011-032) and the Novelli-Pak-Stoyanovskii bijection (Discrete Math. Theoret. Computer Science 1 (1997), 053-067) 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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