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On Covering of Balanced Incomplete Block Designs

Published online by Cambridge University Press:  20 November 2018

Haim Hanani
Haim Hanani*
Affiliation:
Technion, Israel Institute of Technology, Haifa, Israel
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Given a set E of v elements and given positive integers k (k ≤ v) and λ, we understand by balanced incomplete block design (BIBD) B [k, λ, v] a system of blocks (subsets of E) having k elements each such that every pair of elements of E is contained in exactly λ blocks.

A necessary condition for the existence of a design B [k, λ, v] is known to be (4)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 615 - 625
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Bose, R. C. and Shrikhande, S. S., On the falsity of Euler's conjecture about the non-existence of two orthognal Latin squares of order 42 + 2, Proc. Natl. Acad. Sci. U.S., 45 (1959), 734–737.Google Scholar
2. Carmichael, R. D., Groups of finite order (New York, 1956).Google Scholar
3. Fulkerson, D. R. and Ryser, H. J., Width sequences for special classes of (0, 1)-matrices Can. J. Math., 15 (1963), 371–396.Google Scholar
4. Hanani, H., The existence and construction of balanced incomplete block designs, Ann. Math. Stat., 32 (1961), 361–386.Google Scholar
5. Nandi, H. K., On the relation between certain types of tactical configurations, Bull. Calcutta Math. Soc, 37 (1945), 92–94.Google Scholar
6. Tarry, G., Le problème des 36 officiers, C. R. Assoc. Franc. Avan. Sci., 1 (1900), 122–123; 2 (1901), 170-203. Google Scholar