## The Annals of Mathematical Statistics

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

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

#### 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

**Permanent link to this document**

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**

links.jstor.org

#### Citation

Hoffman, A. J. On the Duals of Symmetric Partially-Balanced Incomplete Block Designs. Ann. Math. Statist. 34 (1963), no. 2, 528--531. doi:10.1214/aoms/1177704164. https://projecteuclid.org/euclid.aoms/1177704164