Difference set
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For the set of elements in one set but not another, see Relative complement. For the set of differences of pairs of elements, see Minkowski difference.
In combinatorics, a difference set is a subset of size of a group of order such that every non-identity element of can be expressed as a product of elements of in exactly ways. A difference set is said to be cyclic, abelian, non-abelian, etc., if the group has the corresponding property. A difference set with is sometimes called planar or simple.[1] If is an abelian group written in additive notation, the defining condition is that every non-zero element of can be written as a difference of elements of in exactly ways. The term "difference set" arises in this way.