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Science & Technology, Physical Sciences, Mathematics, Multiple orthogonal polynomial, Nikishin system, Banded Hessenberg matrix, Block Toeplitz matrix, Riemann-Hilbert matrix, Generalized Poincare theorem, Ratio asymptotics, Vector equilibrium problem, Interlacing, Totally positive matrix, ORTHOGONAL POLYNOMIALS, EQUILIBRIUM PROBLEM, ASYMPTOTICS, THEOREM, 0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, 0104 Statistics, Numerical & Computational Mathematics, 4901 Applied mathematics, 4904 Pure mathematics