论文信息 - Mendelsohn directed triple systems

Mendelsohn directed triple systems

Abstract We introduce a class of ordered triple systems which are both Mendelsohn triple systems and directed triple systems. We call these Mendelsohn directed triple systems (MDTS(v,λ)), characterise them, and prove that they exist if and only if λ(v−1)≡0 ( mod 3) . This is the same spectrum as that of regular directed triple systems, of which they are a special case. We also prove that cyclic MDTS(v,λ) exist if and only if λ(v−1)≡0 ( mod 6) . In so doing we simplify a known proof of the existence of cyclic directed triple systems. Finally, we enumerate some ‘small’ MDTS.

Mike J. Grannell | Terry S. Griggs | Kathleen A. S. Quinn | M. Grannell | T. Griggs

[2] Andries E. Brouwer,et al. Optimal Packings of K4's into a Kn , 1979, J. Comb. Theory A.

[3] R. Julian R. Abel,et al. On the Closure of Subsets of {4, 5, ..., 9} which contain {4} , 1997, Ars Comb..

[4] C. Colbourn,et al. The CRC handbook of combinatorial designs , edited by Charles J. Colbourn and Jeffrey H. Dinitz. Pp. 784. $89.95. 1996. ISBN 0-8493-8948-8 (CRC). , 1997, The Mathematical Gazette.

[5] Rose Peltesohn. Eine Lösung der beiden Heffterschen Differenzenprobleme , 1939 .

[7] Ronald C. Mullin,et al. The closure of all subsets of {3, 4, ...10} which include 3 , 1995, Ars Comb..

[8] Hanfried Lenz,et al. Design theory , 1985 .