Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
Aspects of combinatorics include:
- enumerative combinatorics: counting the structures of a given kind and size
- combinatorial designs and matroid theory: deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria
- extremal combinatorics and combinatorial optimization: finding "largest", "smallest", or "optimal" objects
- algebraic combinatorics:
- studying combinatorial structures arising in an algebraic context
- applying algebraic techniques to combinatorial problems