= Single-box up-move
A single-box up-move changes a <partition of an integer> by adding one to row $i$ and subtracting one from row $j>i$, provided the result remains a partition. It increases exactly the partial sums ending between rows $i$ and $j-1$. A partition $\mu$ dominates $\lambda$ precisely when it is obtainable from $\lambda$ by a sequence of these moves: fill the first deficient row from the row at the first return of the cumulative deficit to zero. This preserves the partition inequalities and decreases the distance to $\mu$.
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