Factors of Sparse Polynomials are Sparse

Zeev Dvir; Rafael Mendes de Oliveira

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arXiv · 1404.4834

Factors of Sparse Polynomials are Sparse

Zeev Dvir·Rafael Mendes de Oliveira

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Abstract

This paper was removed due to an error in the proof (Claim 4.12 as stated is not true). The authors would like to thank Ilya Volkovich for pointing out a counterexample to this paper's main result in positive characteristic: If $F$ is a field with prime characteristic $p$, then the polynomial $x_1^p + x_2^p + \ldots + x^n^p$ has the following factor: $(x_1+x_2+ \ldots + x_n)^{p-1}$, which has sparsity $n^p$.

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BibTeX RIS

Zeev Dvir, Rafael Mendes de Oliveira. 2014-05-19. Factors of Sparse Polynomials are Sparse. https://arxiv.org/abs/1404.4834

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