 |
A descending plane partition of order 
is a two-dimensional array (possibly empty) of positive integers
less than or equal to 
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.
 |
The sole descending plane partition of order one is the empty one 
, the two of order two are "2" and 
, and the seven of order three are illustrated above.
In general, the number of descending plane partitions of order 
is equal to the number of 
-bordered alternating
sign matrices: 1, 2, 7, 42, 429, ... (OEIS A005130).
