An integer partition is a way of writing a positive integer as a sum of positive integers, where the order of addends does not matter. For example, the number 4 can be partitioned into 4, 3 + 1, 2 + 2, and 2 + 1 + 1. Each unique combination represents a different partition of the integer. The study of integer partitions is a significant area in combinatorics, a branch of mathematics. The number of partitions of an integer is denoted by p(n), where n is the integer. Integer partitions have applications in number theory, mathematical analysis, and even in computer science for algorithm design.