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An update on the existence of Kirkman triple systems with steiner triple systems as subdesigns
Journal of Combinatorial Designs, 2022AbstractA Kirkman triple system of order , KTS, is a resolvable Steiner triple system on elements. In this paper, we investigate an open problem posed by Doug Stinson, namely the existence of KTS which contain as a subdesign a Steiner triple system of order , an STS. We present several different constructions for designs of this form. As a consequence,
Peter J. Dukes, Esther R. Lamken
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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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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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WILSON SYSTEM FOR TRIPLE REDUNDANCY
International Journal of Wavelets, Multiresolution and Information Processing, 2011A Wilson orthonormal basis was constructed in 1991 by Daubechies, Jaffard and Journé from Gabor tight frame elements, when the redundancy of the Gabor system is 2. In 1994, Auscher gave a characterization of the atoms for which the Wilson system is an orthonormal basis.
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Australas. J Comb., 1994
Summary: An antipodal triple system of order \(v\) is a triple \((V,B,f)\), where \(| V|= v\), \(B\) is a set of cyclically oriented 3-subsets of \(V\), and \(f: V\to V\) is an involution with one fixed point such that: (i) \((V,B\cup f(B))\) is a Mendelsohn triple system. (ii) \(B\cap f(B)= \varnothing\).
Peter B. Gibbons +2 more
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Summary: An antipodal triple system of order \(v\) is a triple \((V,B,f)\), where \(| V|= v\), \(B\) is a set of cyclically oriented 3-subsets of \(V\), and \(f: V\to V\) is an involution with one fixed point such that: (i) \((V,B\cup f(B))\) is a Mendelsohn triple system. (ii) \(B\cap f(B)= \varnothing\).
Peter B. Gibbons +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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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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Constructive Packings of Triple Systems
SIAM Journal on Discrete Mathematics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Triple Graph Grammars or Triple Graph Transformation Systems?
2009Triple graph grammars have been used to specify consistency maintenance between inter-dependent and evolving models at a high level of abstraction. On a lower level, consistency maintenance may be specified by a triple graph transformation system, which takes care of all operational details required for executing consistency maintenance operations.
Thomas Buchmann +2 more
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Embeddings of pure mendelsohn triple systems and pure directed triple systems
Journal of Combinatorial Designs, 1995AbstractIt is proved in this article that the necessary and sufficient conditions for the embedding of a λ‐fold pure Mendelsohn triple system of order v in λ‐fold pure Mendelsohn triple of order u are λu(u − 1) ≡ 0 (mod 3) and u ⩾ 2v + 1. Similar results for the embeddings of pure directed triple systems are also obtained. © 1995 John Wiley & Sons,
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