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E. Jin:
"Outside nested decompositions of skew diagrams and Schur function determinants";
Vortrag: 77th. Séminaire Lotharingien de Combinatoire, Strobl; 12.09.2016 - 14.09.2016.

In this paper we describe the {\em thickened strips} and the {\em outside nested decompositions} of any skew shape $\lambda/\mu$. For any such decomposition $\Phi=(\Theta_1,\Theta_2,\ldots,\Theta_g)$ of the skew shape $\lambda/\mu$ where $\Theta_i$ is a thickened strip for every $i$, if $r$ is the number of boxes that are contained in any two distinct thickened strips of $\Phi$,

we establish a determinantal formula of the function $s_{\lambda/\mu}(X)p_{1^r}(X)$ with the Schur functions of thickened strips as entries, where $s_{\lambda/\mu}(X)$ is the Schur function of the skew shape $\lambda/\mu$ and $p_{1^r}(X)$ is the power sum symmetric function index by the partition $(1^r)$. This generalizes Hamel and Goulden's theorem on the outside decompositions of the skew shape $\lambda/\mu$.

As an application of our theorem, we derive the number of $m$-strip tableaux which was first counted by Baryshnikov and Romik via extending the transfer operator approach due to Elkies.

outside nested decompositions, Schur function, Lattice paths, M-Strip tableaux, Euler numbers