# combinatorial analysis

Combinatorial analysis is the branch of mathematics dealing with subdivisions of sets;
its primary concerns are combinations and permutations and partitions (see partition number). A **partition** of a number *n* is its expression in the form of a sum of positive integers: i.e., setting

*n* = *a*_{1} + *a*_{2} + ... + *a _{n}*.

For example, the number 5 has 7 partitions: (1 + 1 + 1 + 1 + 1), (2 + 1 + 1 + 1), (2 + 2 + 1), (3 + 1 + 1), (3 + 2), (4 + 1), and (5).

By extension **combinatorial topology** is the study of complex
forms in terms of their being built up from combinations of basic geometric
forms.