Combinatorics

Combinatorics is the study of discrete structures in general, and enumeration on discrete structures in particular. For example, the number of three-cycles in a given graph is a combinatoric problem, as is the derivation of a non-recursive formula for the Fibonacci numbers, and so too methods of solving the Rubiks cube. Different kinds of counting problems can be approached by a variety of techniques, such as generating functions or the principle of inclusion-exclusion.