Some composition determinants

Details Some composition determinants Some composition determinants

2005-09-07

arxiv.org/abs/math/0509157v4

Linear Algebra Appl. 416 (2006), 355-364.

Mathematics

Combinatorics

AmS-LaTeX, 9 pages; minor improvements

Scientific paper

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].

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