## The Annals of Mathematical Statistics

### On the Duals of Symmetric Partially-Balanced Incomplete Block Designs

A. J. Hoffman

#### Abstract

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.

#### Article information

Source
Ann. Math. Statist., Volume 34, Number 2 (1963), 528-531.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177704164

Digital Object Identifier
doi:10.1214/aoms/1177704164

Mathematical Reviews number (MathSciNet)
MR146935

Zentralblatt MATH identifier
0114.10904

JSTOR