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Hook-content Formulae for Symplectic and Orthogonal Tableaux

Published online by Cambridge University Press:  20 November 2018

Peter S. Campbell  and
Anna Stokke
Peter S. Campbell
Affiliation:
e-mail: peter s campbell@yahoo.co.uk
Anna Stokke
Affiliation:
Department of Mathematics and Statistics, University of Winnipeg, Winnipeg, MB R3B 2E9 e-mail: a.stokke@uwinnipeg.ca
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Abstract

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By considering the specialisation ${{s}_{\lambda }}(1,\,q,\,{{q}^{2}},\ldots ,\,{{q}^{n-1}})$ 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

05E0505E10symplectic tableauxorthogonal tableauxSchur function

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 3 , 01 September 2012 , pp. 462 - 473
Copyright
Copyright © Canadian Mathematical Society 2012

References

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