Reverse lexicographic order on partitions ($\lambda {<}_R\mu ⟺{\lambda }_i>{\mu }_i\text{ at the first difference}$)

Pad partitions with trailing zeros. In the descending-dictionary convention used for symmetric-function reverse lexicographic ordering, the partition with the larger first differing part precedes the other. This is the reverse of increasing dictionary order on integer partitions, and is a total order. It is distinct from comparing the last differing part in a monomial reverse-lexicographic order.