Asymptotics of Young tableaux in the $(k,\ell)$ hook

Details Asymptotics of Young tableaux in the $(k,\ell)$ hook Asymptotics of Young tableaux in the $(k,\ell)$ hook

2010-07-22

arxiv.org/abs/1007.3833v1

Mathematics

Combinatorics

Scientific paper

The asymptotics of the "$(k,\ell)$ hook" sums $S_{k,\ell}^{(2z)}(n)$ (see~\eqref{the.sums.1}) were calculated in~\cite{berele}. It was recently realized that in~\cite[Section 7]{berele} there are few misprints and certain confusion with regard to the notations, so that the precise asymptotics of $S_{k,\ell}^{(2z)}(n)$ is not clear. Here we add more details and carefully repeat these calculations, which lead to explicit values for the asymptotics of $S_{k,\ell}^{(2z)}(n).$

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