Results 191 to 200 of about 2,403 (227)
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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 \(abe\), \(acf\), \(bdf\), \(cde\).
Eric Mendelsohn +2 more
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On the number of steiner triple systems
Mathematical Notes, 1974We obtain a new lower estimate for the number N(n) of nonisomorphic Steiner triple systems of order n: $$N(n) \geqslant n^{\frac{{n^2 }}{{12}} - O\left( {\frac{{n^2 }}{{logn}}} \right)} .$$ This makes it possible to show that log N(n) is of order n2 log n.
V E Alekseev
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Caps and Colouring Steiner Triple Systems
Designs, Codes and Cryptography, 1998 It 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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Embeddings of partial Steiner triple systems
Journal of Combinatorial Theory - Series A, 2004 Any partial Steiner triple system of order u can be embedded in a Steiner triple system of order v if v equivalent to 1, 3 (mod 6) and v greater than or equal to 3u - 2. (C) 2004 Elsevier Inc.
Darryn Bryant
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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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Enumeration of Steiner triple systems with subsystems
Mathematics of Computation, 2015A Steiner triple system of order v v , an STS(
Östergård, Patric R.J. +3 more
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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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Steiner Triple Systems with High Chromatic Index
SIAM Journal on Discrete Mathematics, 2017 It has been conjectured that every Steiner triple system of order v 6= 7 has chromatic index at most (v + 3)=2 when v = 3 (mod 6) and at most (v + 5)=2 when v = 1 (mod 6).
Charles J Colbourn +2 more
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