Some composition determinants

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We compute two parametric determinants in which rows and columns are indexed by compositions, where in one determinant the entries are products of binomial coefficients, while in the other the entries are products of powers. These results generalize previous determinant evaluations due to the first and third author [SIAM J. Matrix Anal. Appl. 23 (2001), 459--471] and ["A polynomial generalization of the power-compositions determinant," Linear Multilinear Algebra (to appear)], and they prove two conjectures of the second author ["Advanced determinant calculus: a complement," preliminary version].
AmS-LaTeX, 9 pages; minor improvements

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Combinatorics, Classical Analysis and ODEs, Primary 05A19; Secondary 05A10 11C20 15A15

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http://salesiana.dossiersoluciones.com/handle/123456789/102239

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509157
 http://arxiv.org/abs/math/0509157
 Linear Algebra Appl. 416 (2006), 355-364.

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arXiv