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    Unrestricted Partition Function P

    Definition

    P(n), sometimes also denoted p(n), gives the number of ways of writing the integer n as a sum of positive integers, where the order of addends is not considered significant. By convention, partitions are usually ordered from largest to smallest. For example, since 4 can be written 4 | = | 4 | = | 3 + 1 | = | 2 + 2 | = | 2 + 1 + 1 | = | 1 + 1 + 1 + 1, it follows that P(4) = 5. P(n) is sometimes called the number of unrestricted partitions, and is implemented in the Wolfram Language as PartitionsP[n].

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