# Definition:Symmetric Design

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## Definition

A block design with parameters $v, b, r, k, \lambda$ is said to be **symmetric** if $b = v$, and (consequently) $r = k$.

That is, where:

or equivalently:

- the number of points belonging to each block is equal to the number of blocks in which each point is contained.

### Note

The **symmetry** does not mean the incidence matrix is symmetric (it often is not).

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**symmetric design** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**symmetric design**