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Linear
Algebra Appl. 416 (2006), 355-364, the only definitive repository of the content that has been
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Some composition determinants
(9 pages)
Abstract.
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 fourth 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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