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.

单词	Difference set
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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