Results 11 to 20 of about 2,403 (227)
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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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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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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Halving Steiner triple systems
Discrete Mathematics, 1992 A halving of a Steiner triple system (STS) is a partition of its triples into two classes, so that the set of triples in each class are isomorphic as hypergraphs. If such an isomorphism is an automorphism of the STS, the halving is called strong. STS that can be strongly halved are shown to exist if and only if the order is 1 or 9 modulo 24.
Pramod K. Das, Alexander Rosa
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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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Extensions of Steiner Triple Systems [PDF]
Journal of Combinatorial DesignsABSTRACTIn this article, we study extensions of Steiner triple systems by means of the associated Steiner loops. We recognize that the set of Veblen points of a Steiner triple system corresponds to the center of the Steiner loop. We investigate extensions of Steiner loops, focusing in particular on the case of Schreier extensions, which provide a ...
Giovanni Falcone +2 more
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Embedding Steiner triple systems in hexagon triple systems
Discrete Mathematics, 2009 A \textit{Steiner triple} system of order \(n\) (or a triple system) is a pair \((S,T)\), where \(T\) is a collection of edge disjoint triangles, otherwise called triples, which partition the edge set \(K_n\) with vertex set \(S\). It is well known that the spectrum for Steiner triple systems is the set of all \(n \equiv 1\) or \(3 \pmod 6\) and that ...
Charles Curtis Lindner +2 more
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Sequencing partial Steiner triple systems [PDF]
Journal of Combinatorial Designs, 2019 AbstractA partial Steiner triple system of order is sequenceable if there is a sequence of length of its distinct points such that no proper segment of the sequence is a union of point‐disjoint blocks. We prove that if a partial Steiner triple system has at most three point‐disjoint blocks, then it is sequenceable.
Brian Alspach +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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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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