Editing Discrete mathematics (section)

===Combinatorics===
{{Main|Combinatorics}}
Combinatorics studies the ways in which discrete structures can be combined or arranged.
[[Enumerative combinatorics]] concentrates on counting the number of certain combinatorial objects - e.g. the [[twelvefold way]] provides a unified framework for counting [[permutations]], [[combinations]] and [[Partition of a set|partitions]].
[[Analytic combinatorics]] concerns the enumeration (i.e., determining the number) of combinatorial structures using tools from [[complex analysis]] and [[probability theory]]. In contrast with enumerative combinatorics which uses explicit combinatorial formulae and [[generating functions]] to describe the results, analytic combinatorics aims at obtaining [[Asymptotic analysis|asymptotic formulae]].
[[Topological combinatorics]] concerns the use of techniques from [[topology]] and [[algebraic topology]]/[[combinatorial topology]] in [[combinatorics]].
Design theory is a study of [[combinatorial design]]s, which are collections of subsets with certain [[Set intersection|intersection]] properties.
[[Partition theory]] studies various enumeration and asymptotic problems related to [[integer partition]]s, and is closely related to [[q-series]], [[special functions]] and [[orthogonal polynomials]]. Originally a part of [[number theory]] and [[analysis]], partition theory is now considered a part of combinatorics or an independent field.
[[Order theory]] is the study of [[partially ordered sets]], both finite and infinite.