 Solution

Let $\lambda ,\mu ⊢n$ each be a partition of an integer. Pad the lists of parts with zeros and use the dominance order on partitionsThe total sums agree, so only finitely many inequalities matter. This is a partial order: reflexivity and transitivity hold term by term, and equality of all partial sums forces equality of every part, proving antisymmetry. For example $(2,2)⊴(3,1)$. It compares concentration in the top rows, whereas diagram inclusion compares individual cells and is a different relation.