Patterns of dependence among powers of polynomials

Details Patterns of dependence among powers of polynomials Patterns of dependence among powers of polynomials

2001-06-08

arxiv.org/abs/math/0106060v1

Mathematics

Algebraic Geometry

Submitted to Contemp. Math., for the Proceedings of the March 2001 DIMACS workshop on Algorithmic and Quantitative Aspects of

Scientific paper

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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