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In mathematics, the Johnson scheme, named after Selmer M. Johnson, is also known as the triangular association scheme. It consists of the set of all binary vectors X of length ℓ and weight n, such that v = | X | = {\displaystyle v=\left|X\right|={\binom {\ell }{n}}}. Two vectors x, y ∈ X are called ith associates if dist = 2i for i = 0, 1, ..., n. The eigenvalues are given by
where
and Ek is an Eberlein polynomial defined by
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