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A Theorem on Steiner Systems

Published online by Cambridge University Press:  20 November 2018

N. S. Mendelsohn
N. S. Mendelsohn*
Affiliation:
The University of Manitoba, Winnipeg, Manitoba
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1. Definitions and notation. A generalized Steiner system (t-design, tactical configuration) with parameters t, λt, k, v is a system (T, B), where T is a set of v elements, B is a set of blocks each of which is a k-subset of T (but note that blocks bi and bj may be the same k-subset of T) and such that every set of t elements of T belongs to exactly λt of the blocks. If we put λt = u we denote by Su(t, k, v) the collection of all systems with these parameters. Thus Q ∈ Su(t, k, v) means Q = (T, B) is a system with the given parameters. If λt = u = 1, we write S(t, k, v) instead of S1(t, k, v) and refer to the system as a Steiner system. If t = 2, the system is called a balanced incomplete block design.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 5 , 01 October 1970 , pp. 1010 - 1015
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Mendelsohn, N. S., Intersection numbers of t-designs, Notices Amer. Math. Soc. 16 (1969), 984. (Also University of Manitoba mimeographed series.)Google Scholar
2. Riordan, J., Combinatorial identities (Wiley, New York, 1968).Google Scholar
3. Witt, E., Ùber Steinersche Systems, Abh. Math. Sem. Hamburg Univ. 12 (1938), 265–275.Google Scholar