nLab
Steiner system

Steiner systems are combinatorial objects with main applications in finite geometries and finite group theory.

Given positive integers l,n,ml,n,m a Steiner system of type S(l,n,m)S(l,n,m) is a pair of a set SS of cardinality nn and a set of subsets of SS of cardinality mm, called blocks, such that every ll-element subset of SS is in precisely one block.

Nontrivial Steiner systems occur for 1<l<n<m1\lt l\lt n\lt m.

Special cases are S(2,3,n)S(2,3,n)-s called Steiner triple systems and S(3,4,n)S(3,4,n)-s called Steiner quadruple systems.

Last revised on August 30, 2011 at 16:31:48. See the history of this page for a list of all contributions to it.