253 research outputs found
A symmetry theorem on a modified jeu de taquin
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 (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
of the same shape we show that the number of tabloids which result in
if we perform modified jeu de taquin with respect to the total order induced by
is equal to the number of tabloids which result in if we perform
modified jeu de taquin with respect to . This symmetry theorem extends to
skew shapes and shifted skew shapes.Comment: 8 page
Enumeration of Standard Young Tableaux
A survey paper, to appear as a chapter in a forthcoming Handbook on
Enumeration.Comment: 65 pages, small correction
Hook formulas for skew shapes III. Multivariate and product formulas
We give new product formulas for the number of standard Young tableaux of
certain skew shapes and for the principal evaluation of the certain Schubert
polynomials. These are proved by utilizing symmetries for evaluations of
factorial Schur functions, extensively studied in the first two papers in the
series "Hook formulas for skew shapes" [arxiv:1512.08348, arxiv:1610.04744]. We
also apply our technology to obtain determinantal and product formulas for the
partition function of certain weighted lozenge tilings, and give various
probabilistic and asymptotic applications.Comment: 40 pages, 17 figures. This is the third paper in the series "Hook
formulas for skew shapes"; v2 added reference to [KO1] (arxiv:1409.1317)
where the formula in Corollary 1.1 had previously appeared; v3 Corollary 5.10
added, resembles published versio
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