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A partition is a way of writing an Integer 
as a sum of Positive Integers without regard
to order, possibly subject to one or more additional constraints. Particular types of partition functions include the
Partition Function P, giving the number of partitions of a number without regard
to order, and Partition Function Q, giving the number of ways of writing the
Integer as a sum of Positive Integers without regard to order with the constraint that
all Integers in each sum are distinct.
See also Amenable Number, Durfee Square, Elder's Theorem, Ferrers Diagram, Graphical Partition, Partition Function P, Partition Function Q, Perfect Partition, Plane Partition, Set Partition, Solid Partition, Stanley's Theorem
References
Andrews, G. E. The Theory of Partitions. Cambridge, England: Cambridge University Press, 1998.
Dickson, L. E. ``Partitions.'' Ch. 3 in History of the Theory of Numbers, Vol. 2: Diophantine Analysis.
New York: Chelsea, pp. 101-164, 1952.