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• W2047508730 abstract "We propose a new approach to the combinatorial interpretations of linearization coefficient problem of orthogonal polynomials. We first establish a difference system and then solve it combinatorially and analytically using the method of separation of variables. We illustrate our approach by applying it to determine the number of perfect matchings, derangements, and other weighted permutation problems. The separation of variables technique naturally leads to integral representations of combinatorial numbers where the integrand contains a product of one or more types of orthogonal polynomials. This also establishes the positivity of such integrals." @default.
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• W2047508730 date "2013-04-01" @default.
• W2047508730 modified "2023-10-17" @default.
• W2047508730 title "Separation of variables and combinatorics of linearization coefficients of orthogonal polynomials" @default.
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• W2047508730 doi "https://doi.org/10.1016/j.jcta.2012.10.007" @default.
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