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 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.
@article{10_37236_8229,
author = {Marisa Gaetz and Will Hardt and Shruthi Sridhar},
title = {Support equalities among ribbon {Schur} functions},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/8229},
zbl = {1420.05178},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8229/}
}
TY - JOUR
AU - Marisa Gaetz
AU - Will Hardt
AU - Shruthi Sridhar
TI - Support equalities among ribbon Schur functions
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/8229/
DO - 10.37236/8229
ID - 10_37236_8229
ER -
%0 Journal Article
%A Marisa Gaetz
%A Will Hardt
%A Shruthi Sridhar
%T Support equalities among ribbon Schur functions
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8229/
%R 10.37236/8229
%F 10_37236_8229
Marisa Gaetz; Will Hardt; Shruthi Sridhar. Support equalities among ribbon Schur functions. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8229
