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Trails of triples in partial triple systems

Designs, Codes and Cryptography, 2011
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Charles J. Colbourn, Daniel Horsley, Chengmin Wang   +2 more
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Triple Systems are Eulerian

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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An update on the existence of Kirkman triple systems with steiner triple systems as subdesigns

Journal of Combinatorial Designs, 2022
AbstractA 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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Antipodal triple systems [PDF]

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, Eric Mendelsohn, Hao Shen   +2 more
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Tricyclic Steiner Triple Systems

Graphs and Combinatorics, 2010
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Calahan, Rebecca C., Gardner, Robert B., Tran, Quan D.   +2 more
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Rigid Steiner Triple Systems Obtained from Projective Triple Systems

Journal of Combinatorial Designs, 2013
It 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, 2011
A 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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Constructive Packings of Triple Systems

SIAM Journal on Discrete Mathematics, 2017
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Automorphisms of Steiner Triple Systems

IBM Journal of Research and Development, 1960
This 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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Triple Systems

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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