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Difference Set


Let G be a group of group order h and D be a set of k elements of G. If the set of differences d_i-d_j contains every nonzero element of G exactly lambda times, then D is a (h,k,lambda)-difference set in G of order n=k-lambda. If lambda=1, the difference set is called planar. The quadratic residues in the finite field GF(11) form a difference set. If there is a difference set of size k in a group G, then 2(k; 2) must be a multiple of |G|-1, where (k; 2) is a binomial coefficient.

Gordon maintains an index of known difference sets.


See also

Bruck-Ryser-Chowla Theorem, First Multiplier Theorem, Prime Power Conjecture, Set Difference

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References

Gordon, D. M. "The Prime Power Conjecture is True for n<2000000." Electronic J. Combinatorics 1, No. 1, R6, 1-7, 1994. http://www.combinatorics.org/Volume_1/Abstracts/v1i1r6.html.Gordon, D. M. "La Jolla Difference Set Repository." http://www.ccrwest.org/diffsets/diff_sets/index.html.

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Difference Set

Cite this as:

Weisstein, Eric W. "Difference Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DifferenceSet.html

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