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partition


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(of a positive integer)

A partition of the positive integer n is obtained by writing n=n1+n2+…+nk, where n1, n2,…, nk are positive integers, and the order in which n1, n2,…, nk appear is unimportant. The number of partitions of n is denoted by p(n). For example, the partitions of 5 are

5, 4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1, 1+1+1+1+1,

and hence p(5)=7. The values of p(n) for small values of n are as follows:

Subjects: Mathematics.


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