Support Equalities Among Ribbon Schur Functions

Marisa Gaetz, Will Hardt, Shruthi Sridhar
2019 Electronic Journal of Combinatorics  
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 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 ribbon $\alpha$ produces a ribbon $\alpha_{\pi}$ with the same Schur support as $\alpha$; when this occurs for
more » ... en 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 ribbon $\alpha$ to have full equivalence class. Additionally, we prove a separate necessary condition, which we conjecture to be sufficient.
doi:10.37236/8229 fatcat:bsf2uyhguvfuvgvo4nwgftursm