A partition in number theory is a way of writing a number (n) as a sum of positive integers. Each integer is called a summand, or a part, and if the order of the summands matters, then the sum becomes a composition.
The partition function represents the number of possible partitions of a natural number (n), or the number of distinct and order-independent ways of representing n as a sum of natural numbers. For example, the number 4 can be partitioned in five distinct ways: 1 + 3, 1 + 1 + 2, 1 + 2 + 1, 2 + 1 + 1, and 3 + 1. These partitions can be represented visually by a Young Diagram, which is a finite collection of boxes arranged in left-justified rows, with the row lengths decreasing.
Partitioning is taught to young children in order to work with problems that involve large numbers by splitting them into smaller units. Partitioning can be done instead of adding numbers in a column, and it may take a problem such as 79 + 34 = 113 and change it into 70 + 9 + 30 + 4 = 113, or 70 + 30 + 9 + 4 = 100 + 13 = 113.