Steiner systems are combinatorial objects whose main applications are in finite geometries and finite group theory.
Given positive integers a Steiner system of type is a pair of a set of cardinality and a set of subsets of of cardinality , called blocks, such that every -element subset of is in precisely one block.
Nontrivial Steiner systems occur for .
Special cases are the , called Steiner triple systems, and the , called Steiner quadruple systems.
The simple sporadic Mathieu groups arise as automorphism groups of certain Steiner systems. For instance, the largest, , is composed by the automorphisms of .
Last revised on August 27, 2019 at 12:23:03. See the history of this page for a list of all contributions to it.