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Derived Mendelsohn triple systems

Published online by Cambridge University Press:  17 April 2009

Zoran Stojaković
Affiliation:
Institute of Mathematics University of Novi SadTrg D. Obradovića 4 21000 Novi Sad, Yugoslavia
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Mendelsohn triple system of order ν which can be extended to a tetrahedral quadruple system of order ν + 1 we call a derived Mendelsohn triple system. We consider some properties of derived Mendelsohn triple systems and give some results on their existence.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Doyen, J., ‘Constructions of disjoint Steiner triple systems’, Proc. Amer. Math. Soc. 32 (1972), 409416.CrossRefGoogle Scholar
[2]Ganter, B. and Werner, H., ‘Co-ordinatizing Steiner systems’, in Topics on Steiner systems, Annals of Discrete Mathematics 7, 1980, pp. 324.CrossRefGoogle Scholar
[3]Hartman, A. and Phelps, K.T., ‘The spectrum of tetrahedral quadruple systems’, Utilitas Math. 37 (1990), 181188.Google Scholar
[4]Lindner, C.C., ‘On the number of disjoint Mendelsohn triple systems’, J. Combin. Theory Series A 30 (1981), 326330.CrossRefGoogle Scholar
[5]Mendelsohn, E., ‘The smallest non derived triple system is simple as a loop’, Algebra Univeraalis 8 (1978), 256269.CrossRefGoogle Scholar
[6]Mendelsohn, N.S., ‘A natural generalization of Steiner triple systems’, in Computers in number theory (Academic Press, New York, 1971), pp. 323338.Google Scholar
[7]Mendelsohn, N.S., ‘A single groupoid identity for Steiner loops’, Aequationes Math. 6 (1971), 228230.CrossRefGoogle Scholar
[8]Phelps, K.T., ‘A survey of derived triple systems’, in Topics on Steiner systems, Annals of Discrete Mathematics 7, 1980, pp. 105114.CrossRefGoogle Scholar
[9]Quackenbush, R.W., ‘Near boolean algebras I: Combinatorial aspects’, Discrete Math. 10 (1974), 301308.CrossRefGoogle Scholar
[10]Quackenbush, R.W., ‘Algebraic speculations about Steiner systems’, in Topics on Steiner systems, Annals of Discrete Mathematics 7, 1980, pp. 2535.CrossRefGoogle Scholar
[11]Stanton, R.G. and Mendelsohn, N.S., ‘Some results on ordered quadruple systems’, in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computing (Utilitas Math. Publ., 1970), pp. 297309.Google Scholar
[12]Stojaković, Z., ‘Alternating symmetric n-quasigroups’, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 18 (1983), 259272.Google Scholar
[13]Stojaković, Z., ‘A generalization of Mendelsohn triple systems’, Ars Combin. 18 (1984), 131138.Google Scholar
[14]Stojaković, Z. and Madaras, R., ‘On teterahedral quadruple systems’, Utilitas Math. 20 (1986), 1926.Google Scholar