Results 181 to 190 of about 2,160 (213)
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The spectrum of nested Steiner triple systems
Graphs and Combinatorics, 1985A Steiner triple system of order v (STS(v)) is nested if it is possible to add a point to each block and obtain a BIBD(v,4,2). Clearly it is necessary that \(v\equiv 1(mod 6)\). The author points out that, in a sequence of papers, it had been shown that a nested STS(v) is possible whenever \(v\equiv 1(mod 6)\) but with perhaps a few exceptions.
D R Stinson
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Embedding Steiner triple systems into Steiner systems S(2,4,v)
Discrete Mathematics, 2004 We initiate a systematic study of embeddings of Steiner triple systems into Steiner systems S(2,4,v). We settle the existence of an embedding of the unique STS(7) and, with one possible exception, of the unique STS(9) into S(2,4,v). We also obtain bounds
Mariusz Meszka, Alexander Rosa
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The Spectrum of Orthogonal Steiner Triple Systems
Canadian Journal of Mathematics, 1994 AbstractTwo Steiner triple systems (V, 𝓑) and (V, 𝓓) are orthogonal if they have no triples in common, and if for every two distinct intersecting triples {x,y,z} and {x, y, z} of 𝓑, the two triples {x,y,a} and {u, v, b} in (𝓓 satisfy a ≠ b. It is shown here that if v ≡ 1,3 (mod 6), v ≥ 7 and v ≠ 9, a pair of orthogonal Steiner triple systems of order v
Colbourn, Charles J. +4 more
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On 6-sparse Steiner triple systems
Journal of Combinatorial Theory - Series A, 2007 We give the first known examples of 6-sparse Steiner triple systems by constructing 29 such systems in the residue class 7 modulo 12, with orders ranging from 139 to 4447.
T S Griggs
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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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Coloring Steiner Triple Systems
SIAM Journal on Algebraic Discrete Methods, 1982In this paper, several results on the chromatic number of Steiner triple systems are established. A Steiner triple system is a simple 3-uniform hypergraph in which every pair of vertices is connected by exactly one 3-edge. Among other things, we prove that for any $k\geqq 3$ there exists an $n_k $ such that for all admissible $v \geqq n_k $ there ...
de Brandes, Marcia +2 more
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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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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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Representing Graphs in Steiner Triple Systems
Graphs and Combinatorics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dan Archdeacon +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.
Aiden A. Bruen +2 more
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