Topics: Combinatorics

Combinatorics

Combinatorics is a branch of pure mathematics that studies discrete and usually finite objects. It is related to many other areas of mathematics such as algebra, probability theory, ergodic theory and geometry, as well as to applied subjects in computer science and statistical physics.

In combinatorial, a combination is an prescribed size and taken from a given set without a definite order. (An ordered collection of distinct elements would sometimes be called a permutation, but that term is ambiguous.) Given such a set S, a combination of elements of S is just a subset of S, where as always for (sub)sets the order of the elements is not taken into account (two lists with the same elements in different orders are considered to be the same combination).