## Quick Reference

(of a positive integer)

A partition of the positive integer *n* is obtained by writing *n*=*n*_{1}+*n*_{2}+…+*n*_{k}, where *n*_{1}, *n*_{2},…, *n*_{k} are positive integers, and the order in which *n*_{1}, *n*_{2},…, *n*_{k} 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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