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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 new. An S 2,3, n was and still is called a Steiner triple or triad system , while an S 3,4, n is called a Steiner quadruple system , and so on.

With the generalization of the definition, this naming system is no longer strictly adhered to. His proof is non-constructive and, as of , no actual Steiner systems are known for large values of t.

An affine plane of order q can be obtained from a projective plane of the same order by removing one block and all of the points in that block from the projective plane.

Choosing different blocks to remove in this way can lead to non-isomorphic affine planes. An S 3,4, n is called a Steiner quadruple system.

The abbreviation SQS n is often used for these systems. Up to isomorphism, SQS 8 and SQS 10 are unique, there are 4 SQS 14 s and 1,, SQS 16 s.

An S 4,5, n is called a Steiner quintuple system. Sufficient conditions are not known. There is a unique Steiner quintuple system of order 11, but none of order 15 or order The smallest order for which the existence is not known as of is An S 2,3, n is called a Steiner triple system , and its blocks are called triples.

It is common to see the abbreviation STS n for a Steiner triple system of order n. The fact that this condition on n is sufficient for the existence of an S 2,3, n was proved by Raj Chandra Bose [7] and T.

Up to isomorphism, the STS 7 and STS 9 are unique, there are two STS 13 s, 80 STS 15 s, and 11,,, STS 19 s. This is called resolvable and such systems are called Kirkman triple systems after Thomas Kirkman , who studied such resolvable systems before Steiner.

Dale Mesner, Earl Kramer, and others investigated collections of Steiner triple systems that are mutually disjoint i. The corresponding question for finding thirteen different disjoint S 2,3,15 systems was asked by James Sylvester in and answered by RHF Denniston in There is at least one such set of S 2,3,15 but its isomorphism is not known.

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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 ≥ 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. Rebecca Clopath, Manu Buffara and Dalad Kambhu in Graubünden Read more. ReThinkingPaper. Sustainable recycled papers with the Blue Angel from market leader Steinbeis. Become part of a green revolution. Translation for 'Steißbein' in the free German-English dictionary and many other English translations. Steinbeisser was founded in by Jouw Wijnsma and Martin Kullik. In Steinbeisser launched the Experimental Gastronomy initiative based in Amsterdam and active around the world.

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