Partition function (number theory)

In number theory, the partition function p(n) represents the number of possible partitions of a natural number n, which is to say the number of distinct (and order independent) ways of representing n as a sum of natural numbers. For example, 4 can be partitioned in 5 distinct ways

Related Topics:
Number theory - Number - Partitions - Natural number - Sum

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:4, 3 + 1, 2 + 2, 2 + 1 + 1, 1 + 1 + 1 + 1

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So p(4) = 5. By convention p(0) = 1, p(n) = 0 for n negative. Partitions can be graphically visualized with Young diagrams. They occur in a number of branches of mathematics and physics, including the study of symmetric polynomials, the symmetric group and in group representation theory in general.

Related Topics:
Young diagram - Mathematics - Physics - Symmetric polynomial - Symmetric group - Group representation theory

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