The study of counting, arrangement, and selection of discrete structures.
permutations count ordered arrangements; combinations count unordered selections
pigeonhole principle:: if n items are placed in m containers with n > m, at least one container holds more than one item
generating functions encode sequences as coefficients of formal power series
Ramsey theory:: sufficiently large structures inevitably contain ordered substructures
graph enumeration counts distinct graphs and connects to graph theory
binomial coefficients and Pascal's triangle arise in probability and algebra
inclusion-exclusion principle computes sizes of unions via alternating sums of intersections
Related:: number theory, set theory, logic, information theory, game theory