Lesson plan
Difference set
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 non-identity 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 non-zero 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.
Article summary
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 non-identity 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 non-zero 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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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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