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Tricyclic Steiner Triple Systems
Graphs and Combinatorics, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Calahan, Rebecca C. +2 more
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Embedding Partial Steiner Triple Systems
Proceedings of the London Mathematical Society, 1980We prove that a partial Steiner triple system 8 of order n can be embedded in a Steiner triple system T of any given admissible order greater than 4w. Furthermore, if G(S), the missing-edge graph of S, has the property that A(G)
Andersen, L. D. +2 more
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Abelian Steiner Triple Systems
Canadian Journal of Mathematics, 1976A neofield of order v, Nv( + , •), is an algebraic system of v elements including 0 and 1,0 ≠ 1, with two binary operations + and • such that (Nv, + ) is a loop with identity element 0; (Nv*, •) is a group with identity element 1 (where Nv* = Nv\﹛0﹜) and every element of Nv is both right and left distributive (i.e., (y + z)x = yx + zx and x(y + z) = xy
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Anti-mitre steiner triple systems
Graphs and Combinatorics, 1994A \((k,\ell)\)-configuration in a Steiner triple system \((V,B)\), is a subset of \(\ell\) triples from \(B\) whose union is a \(k\)-element subset of \(V\). The Pasch configuration is the \((6,4)\)-configuration on a set \(\{a,b, c,d, e,f\}\) with triples \(abe\), \(acf\), \(bdf\), \(cde\).
Colbourn, Charles J. +3 more
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Rigid Steiner Triple Systems Obtained from Projective Triple Systems
Journal of Combinatorial Designs, 2013It was shown by Babai in 1980 that almost all Steiner triple systems are rigid; that is, their only automorphism is the identity permutation. Those Steiner triple systems with the largest automorphism groups are the projective systems of orders. In this paper, we show that each such projective system may be transformed to a rigid Steiner triple system ...
Grannell, M. J., Knor, M.
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Linearly Derived Steiner Triple Systems
Designs, Codes and Cryptography, 1998A Steiner triple system of order \(n\) \((\text{STS}(n))\) is derived if it can be extended to a Steiner quadruple system of order \(n+1\), i.e. if one can find \(n(n- 1)(n- 3)/24\) quadruples of elements of the STS such that neither of these contains a triple of the STS, and, moreover, each 3-subset which is not a triple of the STS is contained in ...
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Automorphisms of Steiner Triple Systems
IBM Journal of Research and Development, 1960This paper treats the following problem in combinatorial analysis: Find an incomplete balanced block design D with parameters b, v, r, k, and λ = 1, possessing an automorphism group G which is doubly transitive on the elements of D and such that the subgroup H of G fixing all the elements of a block is transitive on the remaining elements.
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Journal of Geometry, 1979
A regular planar Steiner triple system is a Steiner triple system provided with a family of non-trivial sub-systems of the same cardinality (called planes) such that (i) every set of 3 non collinear points is contained in exactly one plane and (ii) for every plane H and every disjoint block B, there are exactly α planes containing B and intersecting H ...
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A regular planar Steiner triple system is a Steiner triple system provided with a family of non-trivial sub-systems of the same cardinality (called planes) such that (i) every set of 3 non collinear points is contained in exactly one plane and (ii) for every plane H and every disjoint block B, there are exactly α planes containing B and intersecting H ...
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Representing Graphs in Steiner Triple Systems
Graphs and Combinatorics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Archdeacon, Dan +2 more
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Caps and Colouring Steiner Triple Systems
Designs, Codes and Cryptography, 1998It has been shown [\textit{R. Hill}, Discrete Math. 22, 111-137 (1978; Zbl 0391.51005)], that the largest cap (collection of points no 3 of which are collinear) in \(\text{PG}(5,3)\) (the projective geometry of dimension \(n\) over the field of order 3) has cardinality 56.
Bruen, Aiden +2 more
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