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An Embedding Theorem for Balanced Incomplete Block Designs

Published online by Cambridge University Press:  20 November 2018

Marshall Hall Jr.  and
W. S. Connor
Marshall Hall Jr.
Affiliation:
Ohio State University
W. S. Connor
Affiliation:
National Bureau of Standards, Washington, D.C.
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From a symmetric balanced incomplete block design we may construct a derived design by deleting a block and its varieties. But a design with the parameters of a derived design may not be embeddable in a symmetric design. Bhattacharya (1) has such an example with λ = 3 . When λ = 1, the derived design is a finite Euclidean plane and this can always be embedded in a corresponding symmetric design which will be a finite projective plane.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 35 - 41
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Bhattacharya, K. N., A new balanced incomplete block design, Science and Culture, 9 (1944), 508.Google Scholar
2. Connor, W. S., Jr., On the structure of balanced incomplete block designs, Ann. Math. Stat., 23 (1952), 57–71.Google Scholar
3. Nandi, H. K., Enumeration of non-isomorphic solutions of balanced incomplete block designs, Sankhya, 7 (1946), 305–312.Google Scholar