Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-14T23:36:43.408Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Bose, R. C. (1942). ‘A note on the resolvability of balanced incomplete block designs’, Sankhya 6, 105–110.Google Scholar
Connor, W. S. (1952), ‘On the structure of balanced incomplete block designs’, Ann. Math. Stat. 23, 57–71.Google Scholar
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