Combinatorics

Combinatorics is a branch of mathematics that studies collections (usually finite) of objects that satisfy specified criteria. In particular, it is concerned with "counting" the objects in those collections (enumerative combinatorics), with deciding when the criteria can be met and then constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), with finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and with finding algebraic structures these objects may have (algebraic combinatorics).

See also

• Combinatorial principles
• Inclusion-exclusion principle
• Method of distinguished element
• Important publications in combinatorics
• List of combinatorics topics
• musical set theory