Johnson scheme

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 ${\displaystyle v=\left|X\right|={\binom {\ell }{n}}}$. Two vectors x, y ∈ X are called ith associates if dist(x, y) = 2i for i = 0, 1, ..., n. The eigenvalues are given by

where

and E_k(x) is an Eberlein polynomial defined by

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