7 | 7 | 6 | 6 | 3 | 1 | 6 | 5 | 4 | 2 | | | 3 | 3 | | | | | 2 | | A descending plane partition of order n is a two-dimensional array (possibly empty) of positive integers less than or equal to n such that the left-hand edges are successively indented, rows are nonincreasing across, columns are decreasing downwards, and the number of entries in each row is strictly less than the largest entry in that row. Implicit in this definition are the requirements that no "holes" are allowed in the array, all rows are flush against the top, and the diagonal element must be filled if any element of its row is filled. The above example shows a decreasing plane partition of order seven.

alternating sign matrix | plane partition