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Some results on a combinatorial problem of Cordes

Published online by Cambridge University Press:  09 April 2009

D. McCarthy  and
G. H. J. van Rees
D. McCarthy
Affiliation:
University of Waterloo, Waterloo, Ontario, Canada
G. H. J. van Rees
Affiliation:
University of Waterloo, Waterloo, Ontario, Canada
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Abstract

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Cordes (1976) introduced the problem of determining the maximum number of resolution classes of a finite set partitioned into equicardinal subsets such that the number of pairs common to any 2 classes is minimized. A later paper of Mullin and Stanton (1976) investigated those conditions under which the configurations were actually BIBD's. They obtained a bound for these special configurations and conjectured it applied in general. We prove this in the present paper. A recursive and a direct construction are also given for a special class of configurations.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 4 , June 1977 , pp. 439 - 452
Copyright
Copyright © Australian Mathematical Society 1977

References

Bose, R. C. (1947), ‘On a resolvable series of balanced incomplete designs’, Sankhyā 8, 249–256.Google Scholar
Cordes, C. (submitted), ‘A new type of combinatorial design’, Canadian Journal of Mathematics.Google Scholar
Mullin, R. C., and Stanton, R. G. (to appear), ‘A characterization of Pseudo-affine designs and their relation to a problem of Cordes’, Annals of Discrete Mathematics.Google Scholar
Wallis, W. D., Street, A. P., and Wallis, J. S. (1972), Combinatorics: Room squares, sum-free sets, Hadamard matrices (Lecture Notes in Mathematics 292, Springer-Verlag, Berlin).CrossRefGoogle Scholar