Differential poset
= Differential poset
{title2=$DU-UD=rI$}
{wiki}
A differential poset is a locally finite graded <partially ordered set> with a unique minimum, finite ranks, and up and down cover operators satisfying $DU-UD=rI$ for a fixed positive integer $r$. The <Young lattice> has $r=1$: distinct equal-rank diagrams have equally many common upper and lower covers, and each diagram has one more upper cover than lower cover.