gen-define-partitions-of-an-integer-and-give-one-short-worked-ex-674e

Define partitions of an integer and give one short worked example.

# Partitions of an Integer ## Definition A **partition** of a positive integer n is a way of writing n as a sum of positive integers, where the order of the summands does not matter. The numbers in the sum are called **parts**. By convention, partitions are usually written in non-increasing order (largest to smallest parts). ## Worked Example **Find all partitions of 4:** The partitions of 4 are: - 4 - 3 + 1 - 2 + 2 - 2 + 1 + 1 - 1 + 1 + 1 + 1 Therefore, there are **5 partitions of 4**. --- **Note:** We write "2 + 2" only once (not "2 + 2" and also "2 + 2" separately), and we don't distinguish "3 + 1" from "1 + 3" since order doesn't matter. The number of partitions grows rapidly; for example, there are 7 partitions of 5, but 42 partitions of 10.