Dictionary order on integer partitions
= Dictionary order on integer partitions
{title2=$\lambda>\mu\iff\lambda_k>\mu_k\text{ at the first difference}$}
Pad partitions with trailing zeros and compare their first unequal parts. A partition is larger in <dictionary order on integer partitions> when that first unequal part is larger. This is a total order, whereas <dominance order on partitions> compares every prefix sum and is generally partial. The <row-column collision lemma> links these two orders.