Abstract view
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Hook-content Formulae for Symplectic and Orthogonal Tableaux
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Published:2011-05-30
Printed: Sep 2012
Peter S. Campbell
Anna Stokke,
Department of Mathematics and Statistics, University of Winnipeg, Winnipeg, MB R3B 2E9
Abstract
By considering the specialisation
$s_{\lambda}(1,q,q^2,\dots,q^{n-1})$ of
the Schur function, Stanley was able to describe a formula for the
number of semistandard Young tableaux of shape $\lambda$ in terms of
the contents and hook lengths of the boxes in the Young diagram.
Using specialisations of symplectic and orthogonal Schur functions,
we derive corresponding formulae,
first given by El Samra and King, for the number of semistandard
symplectic and orthogonal $\lambda$-tableaux.
