combinatorial analysis

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 + ... + 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.

Related category

• COMBINATORICS

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