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On Critical r, λ-Systems

Published online by Cambridge University Press:  20 November 2018

J. Vranch
J. Vranch*
Affiliation:
The University of Western Ontario, London, Ontario, Canada
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Summary

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Critical r, λ-systems are introduced such that any nontrivial r, λ-system must be an extension of some critical system. It is shown that parametric values for which critical systems can exist are restricted to λ(v-1) ≤ r(r-1) and, further, to λ(v-1)r(r-1) if the critical system is extendible.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 2 , 01 June 1976 , pp. 217 - 220
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Ryser, H. J., Combinatorial Mathematics, Wiley, 1963.10.5948/UPO9781614440147CrossRefGoogle Scholar
2. Stanton, R. G. and Mullin, R. C. Inductive Methods for BIBD’s, Ann. Math. Stat., 37 (1966), 1348–1354.CrossRefGoogle Scholar