Steiner System
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High Quality Content by WIKIPEDIA articles! In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design. A Steiner system with parameters l, m, n, written S(l,m,n), is an n-element set S together with a set of m-element subsets of S (called blocks) with the property that each l-element subset of S is contained in exactly one block. A Steiner system with parameters l, m, n is often called simply "an S(l,m,n)". An S(2,3,n) is called a Steiner triple system, and its blocks are called triples. The number of triples is n(n-1)/6. We can define a multiplicatio...
High Quality Content by WIKIPEDIA articles! In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design. A Steiner system with parameters l, m, n, written S(l,m,n), is an n-element set S together with a set of m-element subsets of S (called blocks) with the property that each l-element subset of S is contained in exactly one block. A Steiner system with parameters l, m, n is often called simply "an S(l,m,n)". An S(2,3,n) is called a Steiner triple system, and its blocks are called triples. The number of triples is n(n-1)/6. We can define a multiplication on a Steiner triple system by setting aa = a for all a in S, and ab = c if {a,b,c} is a triple. This makes S into an idempotent commutative quasigroup.
