Editing Combinatorics (section)

===Design theory===
{{Main|Combinatorial design}}

Design theory is a study of [[combinatorial design]]s, which are collections of subsets with certain [[Set intersection|intersection]] properties. [[Block design]]s are combinatorial designs of a special type. This area is one of the oldest parts of combinatorics, such as in [[Kirkman's schoolgirl problem]] proposed in 1850. The solution of the problem is a special case of a [[Steiner system]], which play an important role in the [[classification of finite simple groups]]. The area has further connections to [[coding theory]] and geometric combinatorics.

Combinatorial design theory can be applied to the area of [[design of experiments]].  Some of the basic theory of combinatorial designs originated in the statistician [[Ronald Fisher]]'s work on the design of biological experiments. Modern applications are also found in a wide gamut of areas including [[finite geometry]], [[Tournament|tournament scheduling]], [[Lottery|lotteries]], [[mathematical chemistry]], [[mathematical biology]], [[Algorithm design|algorithm design and analysis]], [[Computer network|networking]], [[group testing]] and [[cryptography]].<ref>{{harvnb|Stinson|2003|loc=pg.1}}</ref>