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Embeddings of pure mendelsohn triple systems and pure directed triple systems
Journal of Combinatorial Designs, 1995AbstractIt is proved in this article that the necessary and sufficient conditions for the embedding of a λ‐fold pure Mendelsohn triple system of order v in λ‐fold pure Mendelsohn triple of order u are λu(u − 1) ≡ 0 (mod 3) and u ⩾ 2v + 1. Similar results for the embeddings of pure directed triple systems are also obtained. © 1995 John Wiley & Sons,
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On Triple Systems with Independent Neighbourhoods
Combinatorics, Probability and Computing, 2005The vertex- and edge-set of a hypergraph \(\mathcal H\) -- only 3-uniform hypergraphs are considered -- are denoted respectively by \(V({\mathcal H})\), \(E({\mathcal H})\); the authors use ``simplified notation'', under which the edge with distinct vertices \(x,y,z\) may be written as a word \(xyz\) (where vertices commute). The neighbourhood \(N(ab)\)
Füredi, Zoltán +2 more
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Triple Graph Grammars or Triple Graph Transformation Systems?
2009Triple graph grammars have been used to specify consistency maintenance between inter-dependent and evolving models at a high level of abstraction. On a lower level, consistency maintenance may be specified by a triple graph transformation system, which takes care of all operational details required for executing consistency maintenance operations.
Thomas Buchmann +2 more
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The spectrum of rotational directed triple systems and rotational Mendelsohn triple systems [PDF]
Summary: Necessary and sufficient conditions for the existence of \(k\)-rotational directed triple systems and \(k\)-rotational Mendelsohn triple systems are derived.
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A class of extended triple systems and numbers of common triples [PDF]
The author studies the case when two extended triple systems have exactly \(k\) blocks in common. Let \(I(v)= \{0,1,\dots, S_v- 3, S_v\}\) where \(S_v= v(v+ 3)/6\) is the number of blocks in an extended triple system. Let \(J(v)\) be the set of integers \(k\) such that there exist two triple systems with \(k\) blocks in common. Then \(J(9)= I(9)- 13\),
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Astrophysics and Space Science, 1985
Triple star systems, especially those in which one star has very small mass may be more common than has been generally considered. Here is summarized some of the recent evidence supporting this possibility.
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Triple star systems, especially those in which one star has very small mass may be more common than has been generally considered. Here is summarized some of the recent evidence supporting this possibility.
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Bicyclic directed triple systems
Ars Comb., 1998The paper is about directed triple systems \(\text{DTS}(v)\) which admit an automorphism with cycles of lengths \(N \leq M\), \(N+M = v\). It is proved that for \(N = M\) necessary and sufficient conditions for the existence of such a directed triple system can be expressed by \(v \equiv 4 \pmod 6\), while for ...
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The algebraic and geometric classification of nilpotent Lie triple systems up to dimension four
Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2022Hani Abdelwahab
exaly

