Combinatorics
What is Combinatorics?
Combinatorics is the study of discrete structures broadly speaking. Most notably, combinatorics involves studying the enumeration (counting) of said structures. For example, the number of three-cycles in a given graph is a combinatorial problem, as is the derivation of a non-recursive formula for the Fibonacci numbers.
Why we use Combinatorics?
Combinatorial problems often make up a good portion of problems found in mathematics competitions and can be approached by a variety of techniques, such as generating functions or the principle of inclusion-exclusion. Combinatorics also has many applications outside of pure mathematics, notably in theoretical computer science, statistics, and various fields of science.
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