gen-explain-partitions-of-an-integer-as-you-would-to-a-capable-s-942b

Explain partitions of an integer as you would to a capable student, in 3-4 sentences.

A partition of a positive integer n is a way of writing it as a sum of positive integers, where the order doesn't matter. For example, the number 4 has five partitions: 4, 3+1, 2+2, 2+1+1, and 1+1+1+1. We usually write partitions in non-increasing order (largest to smallest) to avoid counting the same partition multiple times—so 3+1 and 1+3 are considered the same partition. The number of partitions grows surprisingly quickly; while 4 has just 5 partitions, the number 10 already has 42 partitions!