Integer partitions

Let L denote the positive octant of the regular d-dimensional cubic lattice. The summands in the d-partition are thus nonincreasing in each of the d lattice directions. We agree to suppress all zero labels. A 1-partition is the same as an ordinary partition; a 2-partition is often called a plane partition and a 3-partition is often called a solid partition. Three sample plane partitions of n = 26 are ⎛ ⎜ ⎝ 8 9 9

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