In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and t ≥ 2. A Steiner system with parameters t, k, n, written S(t,k,n), is an n-element set S together with a set of k-element subsets of S (called blocks) with the property that each t-element subset of S is contained in exactly one block. In an alternate notation for block designs, an S(t,k,n) would be a t-(n,k,1) design.

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• In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and t ≥ 2. A Steiner system with parameters t, k, n, written S(t,k,n), is an n-element set S together with a set of k-element subsets of S (called blocks) with the property that each t-element subset of S is contained in exactly one block. In an alternate notation for block designs, an S(t,k,n) would be a t-(n,k,1) design. This definition is relatively modern, generalizing the classical definition of Steiner systems which in addition required that k = t + 1. An S(2,3,n) was (and still is) called a Steiner triple (or triad) system, while an S(3,4,n) was called a Steiner quadruple system, and so on. With the generalization of the definition, this naming system is no longer strictly adhered to. A long-standing problem in design theory was if any nontrivial (t < k < n) Steiner systems have t ≥ 6; also if infinitely many have t = 4 or 5. This was solved in the affirmative by Peter Keevash in 2014. (en)
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• 28016 (xsd:integer)
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• 737194222 (xsd:integer)
dbp:author
• Rowland, Todd and Weisstein, Eric W.
• Jakob Steiner
• Thomas Kirkman
dbp:first
• Thomas
• B.T.
• Jakob
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• Steiner_system
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• Kirkman
• Rumov
• Steiner
dbp:title
• Steiner System
• Steiner system
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• SteinerSystem
dbp:year
• 1847 (xsd:integer)
• 1853 (xsd:integer)
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http://purl.org/linguistics/gold/hypernym
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rdfs:comment
• In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and t ≥ 2. A Steiner system with parameters t, k, n, written S(t,k,n), is an n-element set S together with a set of k-element subsets of S (called blocks) with the property that each t-element subset of S is contained in exactly one block. In an alternate notation for block designs, an S(t,k,n) would be a t-(n,k,1) design. (en)
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• Steiner system (en)
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