The ordinary-partition containment conjecture

Let $\mathcal{P}$ be the set of partitions, let $\mathcal{P}_{\mathrm{2reg}}$ be the set of 2-regular partitions, and let $\operatorname{ORD}:\mathcal{P}\rightarrow\mathcal{P}_{\mathrm{2reg}}$ be the function defined from the first column of the spar tableau. If $\lambda,\nu\in\mathcal{P}$ and $\nu$ is obtained by deleting the last row of $\lambda$, then ordinary-partition containment conjecture.

$$\operatorname{ORD}(\nu)\subseteq\operatorname{ORD}(\lambda).$$

This conjecture concerns the behavior of the ordinary-partition function under deletion of a row and is used to support corresponding containment statements for the associated crystal combinatorics.