Two Remarks on Skew Tableaux

Abstract

This paper contains two results on the number $f^{\sigma/\tau}$ of standard skew Young tableaux of shape $\sigma/\tau$. The first concerns generating functions for certain classes of "periodic" shapes related to work of Gessel-Viennot and Baryshnikov-Romik. The second result gives an evaluation of the skew Schur function $s_{\lambda/\mu}(x)$ at $x=(1,1/2^{2k},1/3^{2k}, \dots)$ for $k=1,2,3$ in terms of $f^{\sigma/\tau}$ for a certain skew shape $\sigma/\tau$ depending on $\lambda/\mu$.