A polynomial generalization of the power-compositions determinant
نویسنده
چکیده
Let C(n, p) be the set of p-compositions of an integer n, i.e., the set of ptuples α = (α1, . . . , αp) of nonnegative integers such that α1+ · · ·+αp = n, and x = (x1, . . . , xp) a vector of indeterminates. For α and β two p-compositions of n, define (x + α) = (x1 + α1) β1 · · · (xp + αp) βp . In this paper we prove an explicit formula for the determinant detα,β∈C(n,p)((x + α) ). In the case x1 = · · · = xp the formula gives a proof of a conjecture by C. Krattenthaler.
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