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Patterns of dependence among powers of polynomials

Bruce Reznick
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Abstract

Let F = {f_1,...,f_r} be a family of polynomials and let the ticket of F, T(F), denote the set of integers m so that ${f_j^m}$ is linearly dependent. We show that |T(F)| \le (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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Bruce Reznick. 2001-06-08. Patterns of dependence among powers of polynomials. https://arxiv.org/abs/math/0106060

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