partitietheorie
Partition theory, known as partitietheorie in Dutch, is a branch of number theory and combinatorics that studies partitions of integers. 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 is irrelevant. For example, the partitions of 4 are 4; 3+1; 2+2; 2+1+1; and 1+1+1+1. The partition function p(n) counts the number of partitions of n, with p(0)=1 by convention.
A central tool is the generating function for partitions: sum_{n≥0} p(n) q^n = ∏_{k≥1} 1/(1 - q^k). This
Growth and refinements: Hardy and Ramanujan showed that p(n) grows roughly like exp(π√(2n/3)) divided by 4n√3; later,
Extensions include partitions with restrictions (distinct parts, odd parts), plane partitions, and combinatorial statistics such as