Simple direct constructions for hybrid triple designs

✍ Scribed by Katherine Heinrich

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 363 KB
• Volume: 97
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(91)90438-8

✦ Synopsis

Heinrich, K., Simple direct constructions for hybrid triple designs, Discrete Mathematics 97 (1991) 223-227. A c-hybrid triple design, c-HTD(u, A), is a partition of the arcs of the complete symmetric digraph in which each arc has multiplicity 1, AD%, into c cyclic triples and Lu(v -1)/3-c transitive triples. We give a simple direct construction for all such designs. Let AD& denote the complete symmetric digraph on u vertices in which each arc has multiplicity A. A cyclic triple is a digraph C with V(C) = {a, b, c} and A(C) = {(a, b), (b, c), (c, a)> (A(C) d enotes the arc-set), and a transitive triple is a digraph T with V(T) = {a, b, c } and A(T) = {(b, a), (b, c), (c, a)}. The cyclic triple will be denoted C(a, b, c) and the transitive triple will be denoted * The author acknowledges the financial support of The Natural Sciences and Engineering Research Council of Canada under grant A7829 and would like to thank University of Otago, Dunedin, New Zealand for the hospitality extended to her during spring 1989 when this paper was prepared.