A

David

Darling

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 = a1 + a2 + ... + an.

 

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.