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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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Journal of Combinatorial Designs, 2016
AbstractAn Euler tour of a hypergraph (also called a rank‐2 universal cycle or 1‐overlap cycle in the context of designs) is a closed walk that traverses every edge exactly once. In this paper, using a graph‐theoretic approach, we prove that every triple system with at least two triples is eulerian, that is, it admits an Euler tour.
Šajna, Mateja, Wagner, Andrew
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AbstractAn Euler tour of a hypergraph (also called a rank‐2 universal cycle or 1‐overlap cycle in the context of designs) is a closed walk that traverses every edge exactly once. In this paper, using a graph‐theoretic approach, we prove that every triple system with at least two triples is eulerian, that is, it admits an Euler tour.
Šajna, Mateja, Wagner, Andrew
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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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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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Southeast Asian Bulletin of Mathematics, 2002
The authors study Krein \(H^*\)-triples systems. They introduce the \(J\)-norm, ideals and tripotents to show, e.g., that the triple product is norm continuous. Semisimple Krein \(H^*\)-triple systems are shown to be an orthogonal direct sum of simple such systems. Separable Krein \(H^*\)-triple systems are discussed.
Rema, P. S. +2 more
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The authors study Krein \(H^*\)-triples systems. They introduce the \(J\)-norm, ideals and tripotents to show, e.g., that the triple product is norm continuous. Semisimple Krein \(H^*\)-triple systems are shown to be an orthogonal direct sum of simple such systems. Separable Krein \(H^*\)-triple systems are discussed.
Rema, P. S. +2 more
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1999
Abstract Triple systems are among the simplest combinatorial designs, and are a natural generalization of graphs. They have connections with geometry, algebra, group theory, finite fields, and cyclotomy; they have applications in coding theory, cryptography, computer science, and statistics.
Charles J Colbourn, Alexander Rosa
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Abstract Triple systems are among the simplest combinatorial designs, and are a natural generalization of graphs. They have connections with geometry, algebra, group theory, finite fields, and cyclotomy; they have applications in coding theory, cryptography, computer science, and statistics.
Charles J Colbourn, Alexander Rosa
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Astrophysics and Space Science, 1985
Triple star systems, especially those in which one star has very small mass may be more common than has been generally considered. Here is summarized some of the recent evidence supporting this possibility.
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Triple star systems, especially those in which one star has very small mass may be more common than has been generally considered. Here is summarized some of the recent evidence supporting this possibility.
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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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Israel Journal of Mathematics, 1993
Hanani triple systems on \(v \equiv 1 \pmod 6\) elements are Steiner triple systems having \((v-1)/2\) pairwise disjoint almost parallel classes (sets of pairwise disjoint triples that span \(v-1\) elements), and the remaining triples form a parallel class.
Vanstone, S. A. +7 more
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Hanani triple systems on \(v \equiv 1 \pmod 6\) elements are Steiner triple systems having \((v-1)/2\) pairwise disjoint almost parallel classes (sets of pairwise disjoint triples that span \(v-1\) elements), and the remaining triples form a parallel class.
Vanstone, S. A. +7 more
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