Plane Partition
A two-dimensional array of Integers nonincreasing both left to right and top to bottom which addup to a given number, i.e., 
and 
. For example, a planar partition of22 is given by
The Generating Function for the number
of planar partitions of 
is
(Sloane's A000219, MacMahon 1912b, Beeler et al. 1972, Bender and Knuth 1972). The concept of planar partitionscan also be generalized to cubic partitions.See also Partition, Solid Partition
References
Beeler, M.; Gosper, R. W.; and Schroeppel, R. Item 18 in HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972. Bender, E. A. and Knuth, D. E. ``Enumeration of Plane Partitions.'' J. Combin. Theory Ser. A. 13, 40-54, 1972. Knuth, D. E. ``A Note on Solid Partitions.'' Math. Comput. 24, 955-961, 1970. MacMahon, P. A. ``Memoir on the Theory of the Partitions of Numbers. V: Partitions in Two-Dimensional Space.'' Phil. Trans. Roy. Soc. London Ser. A 211, 75-110, 1912a. MacMahon, P. A. ``Memoir on the Theory of the Partitions of Numbers. VI: Partitions in Two-Dimensional Space, to which is Added an Adumbration of the Theory of Partitions in Three-Dimensional Space.'' Phil. Trans. Roy. Soc. London Ser. A 211, 345-373, 1912b. MacMahon, P. A. Combinatory Analysis, Vol. 2. New York: Chelsea, 1960. Sloane, N. J. A. SequenceA000219/M2566in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
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