Modifications of the “central-method” to construct Steiner triple systems
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چکیده
منابع مشابه
Modifications of the "central-method" to construct Steiner triple systems
Let V with IV1 = v be a finite set and B a set of 3-subsets of V. The elements of V are called points, those of B lines. If any 2-subset of V is contained in exactly one line, then the pair (V, B) is called a Steiner triple system of order V, in short STS(u). Each point lies on exactly r = i(v 1) lines and we have JB1 = b = &(v 1). The condition v = 7, 9 + 6n, IZ E No, is necessary and sufficie...
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A Steiner triple system of order v (briefly STS(v)) is a pair (X, B), where X is a v-element set and B is a collection of 3-subsets of X (triples), such that every pair of X is contained in exactly one triple of B. It is well known that a necessary and sufficient condition for a STS(v) to exist is that v#1 or 3 (mod 6). An r-coloring of a STS(v) is a map , : X [1, ..., r] such that at least two...
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Abstract: Steiner triple systems are among the simplest and most intensively studied combinatorial designs. Their origins go back to the 1840s, and there exists by now a sizeable literature on the topic. In 1980, Babai proved that almost all Steiner triple systems have no nontrivial automorphism. On the other hand, there exist Steiner triple systems with large automorphism groups. We will discu...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1989
ISSN: 0012-365X
DOI: 10.1016/0012-365x(89)90374-9