Results 11 to 20 of about 2,160 (213)
Bicyclic Steiner triple systems
Discrete Mathematics, 1994 A permutation \(\pi\) of a \(v\)-element set is said to be of type \([\pi]=[p_ 1,p_ 2,\ldots,p_ v]\) if the disjoint cyclic decomposition of \(\pi\) contains \(p_ i\) cycles of length \(i\). Thus a cyclic Steiner triple system STS\((v)\) is one admitting an automorphism of type \([0,0,\ldots,0,1]\). A bicyclic Steiner triple system is defined to be one
Calahan-Zijlstra, Rebecca +1 more
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Steiner Triple Systems with an Involution
European Journal of Combinatorics, 1987 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alan Hartman, Dean G. Hoffman
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Rotational Steiner triple systems
Discrete Mathematics, 1982 AbstractA Steiner triple system S(v) of order v is said to be k-rotational if it admits an automorphism consisting of a single fixed element and exactly k (v−1)k-cycles.In this paper we obtain the necessary and sufficient condition for the existence of 3· and 4-rotational Steiner triple systems.
Cho, Chung Je
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Equitable embeddings of steiner triple systems
Journal of Combinatorial Theory, Series A, 1996 An \(n\)-colouring of a Steiner triple system \(\text{STS}(v)\) is a map which assigns one colour, from a set of \(n\) given colours, to each point in such a way that no triple is monochromatic. An STS is \(r\)-chromatic if it can be \(r\)-coloured but not \((r- 1)\)-coloured.
Charles J. Colbourn +2 more
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Balanced Steiner Triple Systems
Journal of Combinatorial Theory, Series A, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Charles J. Colbourn +2 more
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On reverse Steiner triple systems
Discrete Mathematics, 1972 AbstractThe existence of reverse Steiner triple systems (i.e. Steiner triple systems with a given involutory automorphism of special type) is investigated. It is shown that such a system exists for all orders n if n 1 or 3 or 9 (mod 24) except possibly for n = 25.
Rosa, Alexander
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Discrete Mathematics, 1997 A set of blocks of the form \(\{a,x,y\}, \{a,z,w\}, \{b,x,w\}, \{b,z,y\}\) in a Steiner triple system STS\((v)\) is called a Pasch configuration. Replacing these blocks by \(\{b,x,y\}, \{b,z,w\}, \{a,x,w\}, \{a,z,y\}\) produces a new STS\((v)\), which may or may not be isomorphic to the original design. This paper contributes to an investigation of the
Mike J. Grannell +2 more
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Some derived steiner triple systems
Discrete Mathematics, 1976 In this paper certain properties of Steiner triple systems are shown to be sufficient to ensure that it is a derived triple system. In particular it is shown that whenever a Steiner triple system (S, t) of order 2v+1 contains a partial subsystem (V, k) of order v that can be embedded in a derived triple system (V,) where ||=βk|+1, then the Steiner ...
Phelps, Kevin T.
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Identical twin Steiner triple systems [PDF]
Australas. J Comb., 2016 Two Steiner triple systems, each containing precisely one Pasch configuration which, when traded, switches one system to the other, are called twin Steiner triple systems. If the two systems are isomorphic the systems are called identical twins. Hitherto, identical twins were only known for orders 21, 27 and 33.
Grannell, M. J., Lovegrove, G. J.
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Enumerating Steiner triple systems
Journal of Combinatorial Designs, 2023 AbstractSteiner triple systems (STSs) have been classified up to order 19. Earlier estimations of the number of isomorphism classes of STSs of order 21, the smallest open case, are discouraging as for classification, so it is natural to focus on the easier problem of merely counting the isomorphism classes.
Östergård +2 more
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