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Resolvable (r, λ)-designs and the Fisher inequality

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

S. A. Vanstone
S. A. Vanstone
Affiliation:
St. Jerome's College University of WaterlooWaterloo, Ontario, Canada
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Abstract

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It is well known that in any (v, b, r, k, λ) resolvable balanced incomplete block design that b≧ ν + r − l with equality if and only if the design is affine resolvable. In this paper, we show that a similar inequality holds for resolvable regular pairwise balanced designs ((ρ, λ)-designs) and we characterize those designs for which equality holds. From this characterization, we deduce certain results about block intersections in (ρ, λ)-designs.

MSC classification

Secondary: 05B30: Other designs, configurations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 4 , December 1979 , pp. 471 - 478
Copyright
Copyright © Australian Mathematical Society 1979

References

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Fisher, R. A. (1940), ‘An examination of the different possible solutions of a problem in incomplete blocks’, Ann. Eugenics 10, 52–75.CrossRefGoogle Scholar
McCarthy, D. and Vanstone, S. A. (1979), ‘On the structure of regular pairwise balanced designs’, Discrete Math. 25, 237–244.Google Scholar
Ray-Chaudhuri, D. K. and Wilson, R. M. (1979), ‘On t-designs’, Osaka Journal of Math. (to appear).Google Scholar