Patterns of dependence among powers of polynomials
Abstract
Let F = f1,...,fr be a family of polynomials and let the ticket of F, T(F), denote the set of integers m so that fjm is linearly dependent. We show that |T(F)| (r-1)(r-2)/2 and present many concrete examples, including one with r=6 and T(F) = 1,2,3,4,8,14.
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