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1. CMB 2011 (vol 55 pp. 462)
Hook-content Formulae for Symplectic and Orthogonal Tableaux 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 Categories:05E05, 05E10 |
2. CMB 2006 (vol 49 pp. 281)
Correction to a Theorem on Total Positivity A well-known theorem states that if $f(z)$ generates a PF$_r$
sequence then $1/f(-z)$ generates a PF$_r$ sequence. We give two
counterexamples
which show that this is not true, and give a correct version of the theorem.
In the infinite limit the result is sound: if $f(z)$ generates a PF
sequence then $1/f(-z)$ generates a PF sequence.
Keywords:total positivity, Toeplitz matrix, PÃ³lya frequency sequence, skew Schur function Categories:15A48, 15A45, 15A57, 05E05 |