High Quality Content by WIKIPEDIA articles! In mathematics, association schemes are structures that appear in many different forms in the fields of combinatorics and statistics. Their theory is one of the branches of algebraic combinatorics. Two points x and y are called ith associates if left(x,yright) in R_{i}. The definition states that if x and y are ith associates so are y and x. Every pair of points are ith associates for exactly one i. Each point is its own zeroth associate while distinct points are never zeroth associates. If x and y are kth associates then the number of points z which are both i-th associates of x and j-th associates of y is a constant cijk.

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