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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

Information

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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