Zero-patterns of polynomials and Newton polytopes

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:102

Article

Lauder, AGB

关键词: multivariate polynomial;    zero-pattern;    Newton polytope;    hypersurface;    sign-pattern;   

DOI  :  10.1016/S0097-3165(03)00007-4

来源: Elsevier

【 摘 要 】

We present an upper bound on the number of regions into which affine space or the torus over a field may be partitioned by the vanishing and non-vanishing of a finite collection of multivariate polynomials. The bound is related to the number of lattice points in the Newton polytopes of the polynomials, and is optimal to within a factor depending only on the dimension (assuming suitable inequalities hold amongst the relevant parameters). This refines previous work by different authors. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

Free