Patterns of dependence among powers of polynomials
Algebraic Geometry
2007-05-23 v1 Complex Variables
Number Theory
Rings and Algebras
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 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}.
Cite
@article{arxiv.math/0106060,
title = {Patterns of dependence among powers of polynomials},
author = {Bruce Reznick},
journal= {arXiv preprint arXiv:math/0106060},
year = {2007}
}
Comments
Submitted to Contemp. Math., for the Proceedings of the March 2001 DIMACS workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science. The preprint is 25 pp. and a few typos have been corrected from a circulated version