Journal article

Zero-patterns of polynomials and Newton polytopes

Abstract:: 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.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Lauder, A. (2003). Zero-patterns of polynomials and Newton polytopes. Journal of Combinatorial Theory, Series A, 102(1), 10–15.

MLA Style

Lauder, A. “Zero-Patterns of Polynomials and Newton Polytopes.” Journal of Combinatorial Theory, Series A, Publisher's version, vol. 102, no. 1, 2003, pp. 10–15.

Chicago Style

Lauder, A. 2003. “Zero-Patterns of Polynomials and Newton Polytopes.” Journal of Combinatorial Theory, Series A 102 (1): 10–15.
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Files:: 1-s2.0-S0097316503000074-main.pdf

(Preview, Version of record, pdf, 137.7KB, Terms of use)

Publisher copy:: 10.1016/S0097-3165(03)00007-4

Authors

+ Lauder, A More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Computer Science
Role:: Author

+ Engineering and Physical Sciences Research Council More from this funder

Funding agency for:: Lauder, A
Grant:: GR/N35366/01

Publisher:: Elsevier
Journal:: Journal of Combinatorial Theory, Series A More from this journal
Volume:: 102
Issue:: 1
Pages:: 10-15
Publication date:: 2003-04-01
Edition:: Publisher's version
DOI:: 10.1016/S0097-3165(03)00007-4
ISSN:: 0009-7316

Language:: English
Keywords:: multivariate polynomial

Newton polytope

hypersurface

zero-pattern

sign-pattern
Subjects:: Mathematics

Combinatorics
UUID:: uuid:16f16129-3545-42c3-858a-5d1649f6f823
Local pid:: ora:8743
Deposit date:: 2014-07-08
ARK identifier:: ark:/29072/ora_16f16129354542c3858a5d1649f6f823

Terms of use

Copyright holder:: Elsevier Science
Copyright date:: 2003
Notes:: Copyright 2003 Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0/

Licence:: Other

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