1 Answers
In combinatorics, a {\displaystyle } difference set is a subset D {\displaystyle D} of size k {\displaystyle k} of a group G {\displaystyle G} of order v {\displaystyle v} such that every nonidentity element of G {\displaystyle G} can be expressed as a product d 1 d 2 − 1 {\displaystyle d_{1}d_{2}^{-1}} of elements of D {\displaystyle D} in exactly λ {\displaystyle \lambda } ways. A difference set D {\displaystyle D} is said to be cyclic, abelian, non-abelian, etc., if the group G {\displaystyle G} has the corresponding property. A difference set with λ = 1 {\displaystyle \lambda =1} is sometimes called planar or simple. If G {\displaystyle G} is an abelian group written in additive notation, the defining condition is that every nonzero element of G {\displaystyle G} can be written as a difference of elements of D {\displaystyle D} in exactly λ {\displaystyle \lambda } ways. The term "difference set" arises in this way.