Hook-content formulae for symplectic and orthogonal tableaux

Details Hook-content formulae for symplectic and orthogonal tableaux Hook-content formulae for symplectic and orthogonal tableaux

2007-10-22

arxiv.org/abs/0710.4155v1

Mathematics

Combinatorics

14 pages

Scientific paper

By considering the specialisation $s_{\lambda}(1,q,q^2,...,q^{n-1})$ of the Schur function, Stanley was able to describe a formula for the number of semistandard Young tableaux of shape $\lambda$ in terms of two properties of the boxes in the diagram for $\lambda$. 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.

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