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
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The symmetry does not mean the incidence matrix is symmetric (it often is not).
This article, or a section of it, needs explaining. In particular: Why $b = v$ has as a consequence $r = k$. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code. |
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): symmetric design
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): symmetric design