منابع مشابه
Repeated blocks in indecomposable twofold triple systems
A Steiner triple system (STS) (a twofold triple system (TTS)) is a pair (V, B) where V is a v-set, and B is a collection of 3-subsets of V called blocks or triples such that every 2-subset of V is contained in exactly one [exactly two] blocks. The number v is called the order of the STS or TI'S. It is well-known that an STS of order v exists if and only if v 1 or 3 (mod 6), and a T r s of order...
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Cyclically Indecomposable Triple Systems that are Decomposable Martin Grüttmüller Institut für Mathematik, Universität Rostock In this talk, we construct, by using Skolem-type and Rosa-type sequences, cyclically indecomposable two-fold triple systems TS2(v) for all admissible orders. We also investigate exhaustively the cyclically indecomposable triple systems TSλ(v) for λ = 2, v ≤ 33 and λ = 3...
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In 2000, Rees and Shalaby constructed simple indecomposable two-fold cyclic triplesystems for all v ≡ 0, 1, 3, 4, 7, and 9 (mod 12) where v = 4 or v ≥ 12, using Skolem-type sequences.We construct, using Skolem-type sequences, three-fold triple systems having theproperties of being cyclic, simple, and indecomposable for all admissible orders v, withsome possible exception...
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An extended triple system (a twofold extended triple system) with no idempotent element (ETS, TETS respectively) is a pair (V, B) where V is a v-set and B is a collection of unordered triples, called blocks, of type {x,y,z} or {x,x,y}, such that each pair (whether distinct or not) is contained in exactly one (respectively, exactly two) blocks. For example, in the block {x, x, y}, the occurrence...
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We give a new proof that there are arbitrarily large indecomposable abelian groups; moreover, the groups constructed are absolutely indecomposable, that is, they remain indecomposable in any generic extension. However, any absolutely rigid family of groups has cardinality less than the partition cardinal κ(ω). Added December 2004: The proofs of Theorems 0.2 and 0.3 are not correct, and the clai...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1974
ISSN: 0012-365X
DOI: 10.1016/0012-365x(74)90063-6