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Howell Design


Let S be a set of n+1 symbols, then a Howell design H(s,2n) on symbol set S is an s×s array H such that

1. Every cell of H is either empty or contains an unordered pair of symbols from S,

2. Every symbol of S occurs once in each row and column of H, and

3. Every unordered pair of symbols occurs in at most one cell of H.


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References

Colbourn, C. J. and Dinitz, J. H. (Eds.). "Howell Designs." Ch. 26 in CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, pp. 381-385, 1996.

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Howell Design

Cite this as:

Weisstein, Eric W. "Howell Design." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HowellDesign.html

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