Another involution principle-free bijective proof of Stanley's hook-content formula
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, 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.
Cite
@article{arxiv.math/9807068,
title = {Another involution principle-free bijective proof of Stanley's hook-content formula},
author = {Christian Krattenthaler},
journal= {arXiv preprint arXiv:math/9807068},
year = {2007}
}
Comments
23 pages, AmS-TeX