Johnson scheme
Encyclopedia
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
. Two vectors x, y ∈ X are called ith associates if dist(x, y) = 2i for i = 0, 1, ..., n. The eigenvalues are given by
Selmer M. Johnson
Selmer Martin Johnson was an American mathematician, a researcher at the RAND Corporation.-Biography:Johnson was born on May 21, 1916 in Buhl, Minnesota. He earned a B.A. and then an M.A. in mathematics from the University of Minnesota in 1938 and 1940 respectively...
, is also known as the triangular association scheme
Association scheme
The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance. In mathematics, association schemes belong to both algebra and combinatorics. Indeed, in algebraic combinatorics, association schemes provide a unified approach to many topics,...
. It consists of the set of all binary vectors X of length ℓ and weight n, such that
. Two vectors x, y ∈ X are called ith associates if dist(x, y) = 2i for i = 0, 1, ..., n. The eigenvalues are given by-
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where
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and Ek(x) is an Eberlein polynomial defined by
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