Partitions of integers

Partitions of integers involve breaking down a whole number into smaller, positive parts that add up to the original number. For example, the number 4 can be partitioned as 4, 3+1, 2+2, 2+1+1, or 1+1+1+1. The focus is on listing all possible ways to represent the number as sums of positive integers, often with consideration of order or grouping. This concept is fundamental in combinatorics and number theory, helping analyze how numbers can be expressed and related to other mathematical structures.