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June, 1963 On the Duals of Symmetric Partially-Balanced Incomplete Block Designs
A. J. Hoffman
Ann. Math. Statist. 34(2): 528-531 (June, 1963). DOI: 10.1214/aoms/1177704164


It is shown that, under certain hypotheses, the dual of a symmetric partially balanced incomplete block design with $m$ associate classes is also a PBIB design with $m$ associate classes and all parameters the same as before. In the case $m = 1$, and in the case that the design is group divisible, these hypotheses coincide with assumptions previously known to be sufficient to ensure duality. To show that some hypotheses are needed for duality, an example is given of a group divisible design whose dual is not a group divisible design.


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A. J. Hoffman. "On the Duals of Symmetric Partially-Balanced Incomplete Block Designs." Ann. Math. Statist. 34 (2) 528 - 531, June, 1963.


Published: June, 1963
First available in Project Euclid: 27 April 2007

zbMATH: 0114.10904
MathSciNet: MR146935
Digital Object Identifier: 10.1214/aoms/1177704164

Rights: Copyright © 1963 Institute of Mathematical Statistics

Vol.34 • No. 2 • June, 1963
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