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# Hook-content Formulae for Symplectic and Orthogonal Tableaux

Published:2011-05-30
Printed: Sep 2012
• Peter S. Campbell
• Anna Stokke,
Department of Mathematics and Statistics, University of Winnipeg, Winnipeg, MB R3B 2E9
 Format: LaTeX MathJax PDF

## 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.
 Keywords: symplectic tableaux, orthogonal tableaux, Schur function
 MSC Classifications: 05E05 - Symmetric functions and generalizations 05E10 - Combinatorial aspects of representation theory [See also 20C30]

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