An integer partition is a way of expressing 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 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, and 2 + 2. Each unique combination represents a different partition of the integer. The study of integer partitions is a significant topic 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 various fields, including number theory and mathematical analysis.