2001/12/23 by Ilse Fischer, Fischer, Ilse
Mathematics · #Mathematics and Applications #math.CO
paper · pdf · doi:10.48550/arxiv.math/0112263
8 pages
arxiv created 2001/12/23 · arxiv updated 2009/11/30
For their bijective proof of the hook-length formula for the number of standard tableaux of a fixed shape Novelli, Pak and Stoyanovskii define a modified jeu de taquin which transforms an arbitrary filling of the Ferrers diagram with 1,2,...,n (tabloid) into a standard tableau. Their definition relies on a total order of the cells in the Ferrers diagram induced by a special standard tableau, however, this definition also makes sense for the total order induced by any other standard tableau. Given two standard tableaux P,Q of the same shape we show that the number of tabloids which result in P if we perform modified jeu de taquin with respect to the total order induced by Q is equal to the number of tabloids which result in Q if we perform modified jeu de taquin with respect to P. This symmetry theorem extends to skew shapes and shifted skew shapes.