一个正整数可以写成一些正整数的和。在数论上，跟这些和式有关的问题称为整数分拆、整数剖分、整数分割、分割数或切割数。其中最常见的问题就是给定正整数，求不同数组的数目，符合下面的条件：

分割函数p(n)是求符合以上第一、二个条件的数组数目。

In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.) For example, 4 can be partitioned in five distinct ways: