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
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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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