##### 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
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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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