Enumerative combinatorics

Summary

Enumerative combinatorics is the part of combinatorics that counts finite structures, see the definition. It asks for the number of objects of size $n$ in a family, as a function of $n$. Its answers take the form of closed formulas, recurrence relations, generating functions or asymptotic estimates. Its tools range from bijections and the inclusion-exclusion principle to complex analysis in analytic combinatorics.