Support Equalities Among Ribbon Schur Functions

Marisa Gaetz, Will Hardt, Shruthi Sridhar

Published 2017-09-09Version 1

In 2007, McNamara proved that two skew shapes can have the same Schur support only if they have the same number of $k\times \ell$ rectangles as subdiagrams. This implies that two connected ribbons can have the same Schur support only if one is obtained by permuting row lengths of the other. We present substantial progress towards classifying when a permutation $\pi \in S_m$ of row lengths of a connected ribbon $\alpha$ produces a ribbon $\alpha_{\pi}$ with the same Schur support as $\alpha$; when this occurs for all $\pi \in S_m$, we say that $\alpha$ has "full equivalence class." Our main results include a sufficient condition for a connected ribbon $\alpha$ to have full equivalence class. Additionally, we prove a separate necessary condition, which we conjecture to be sufficient.