Tricyclic Steiner Triple Systems with 1-Rotational Subsystems
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Tricyclic Steiner Triple Systems with 1-Rotational Subsystems by
منابع مشابه
The 2-rotational Steiner triple systems of order 25
Chee, Y.M. and G.F. Royle, The 2rotational Steiner triple systems of order 25, Discrete Mathematics 97 (1991) 93-100. In this paper, we enumerate the 2-rotational Steiner triple systems of order 25. There are exactly 140 pairwise non-isomorphic such designs. All these designs have full automorphism groups of order 12. We also investigate the existence of subsystems and quadrilaterals in these d...
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It is shown that for v ≡ 1 or 3 (mod 6), every pair of Heffter difference sets modulo v gives rise to a biembedding of two 2-rotational Steiner triple systems of order 2v + 1 in a nonorientable surface. AMS classification: 05C10.
متن کاملClassroom note: Some partitions of S(2, 3, v2) and S(2, 4, 2)
Introduction The aim of this note is to provide a Steiner triple system STS( v ) which admits a partition into v STS( v) for every v 1 or 3 (mod 6). The STS( v ) obtained in this way will also contain ~v( v 1) subsystems of order 3v. An analogous construction is provided of an S(2, 4, v ) with a partition into v S(2, 4, v)'s in the case v 1 (mod 12). The Steiner system constructed here will als...
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A Steiner triple system of order v (briefly STS(v)) is 1-rotational under G if it admits G as an automorphism group acting sharply transitively on all but one point. The spectrum of values of v for which there exists a 1-rotational STS(v) under a cyclic, an abelian, or a dicyclic group, has been established in Phelps and Rosa (Discrete Math 33:57–66, 1981), Buratti (J Combin Des 9:215–226, 2001...
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There are 172,248 Steiner triple systems of order 19 having a nontrivial automorphism group. Computational methods suitable for generating these designs are developed. The use of tactical configurations in conjunction with orderly algorithms underlies practical techniques for the generation of the designs, and the subexponential time isomorphism technique for triple systems is improved in pract...
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