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Maximal arcs and group divisible designs

Published online by Cambridge University Press:  17 April 2009

Alan Rahilly
Alan Rahilly
Affiliation:
Department of MathematicsUniversity of QueenslandSt Lucia Qld 4067Australia
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Abstract

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The existence of maximal arcs of a certain type in symmetric designs is shown to yield semiregular group divisible designs whose duals are also semiregular group divisible. Two infinite families of such group divisible designs are constructed. The group divisible designs in these families are, in general, not symmetric.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 2 , April 1990 , pp. 223 - 229
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Bose, R.C., ‘Symmetric group divisible designs with the dual property’, J. Statist. Plann. Inference 1 (1977), 87–101.CrossRefGoogle Scholar
[2]Bose, R.C. and Connor, W.S., ‘Combinatorial properties of group divisible incomplete block designs’, Ann. Math. Statist. 23 (1952), 367–383.CrossRefGoogle Scholar
[3]Dembowski, P., Finite Geometries (Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1968).CrossRefGoogle Scholar
[4]Mitchell, C.J., ‘Group divisible designs with dual properties’, Mitt. Math. Sem. Giessen 165 (1984), 105–117.Google Scholar
[5]Morgan, E.J., ‘Arcs in block designs’, Ars Combin. 4 (1977), 3–16.Google Scholar