This material has been published in Linear Algebra Appl. 416 (2006), 355-364, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Elsevier. This material may not be copied or reposted without explicit permission.

Josep Maria Brunat Blay, Christian Krattenthaler, Alain Lascoux and Antonio Montes

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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