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词汇 Difference set
分类 英语词汇 英语翻译词典
释义

Difference set

英语百科

Difference set

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 (v,k,\lambda) difference set is a subset D of size k of a group G of order v such that every nonidentity element of G can be expressed as a product d_1d_2^{-1} of elements of D in exactly \lambda ways. A difference set D is said to be cyclic, abelian, non-abelian, etc., if the group G has the corresponding property. A difference set with \lambda = 1 is sometimes called planar or simple. If G is an abelian group written in additive notation, the defining condition is that every nonzero element of G can be written as a difference of elements of D in exactly \lambda ways. The term "difference set" arises in this way.

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