Polynomials over structured grids

IF 0.9 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Combinatorics, Probability & Computing Pub Date : 2021-10-11 DOI:10.1017/s0963548322000232

B. Nica

引用次数: 3

Abstract

We study multivariate polynomials over ‘structured’ grids. Firstly, we propose an interpretation as to what it means for a finite subset of a field to be structured; we do so by means of a numerical parameter, the nullity. We then extend several results – notably, the Combinatorial Nullstellensatz and the Coefficient Theorem – to polynomials over structured grids. The main point is that the structure of a grid allows the degree constraints on polynomials to be relaxed.

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结构网格上的多项式

我们研究“结构化”网格上的多元多项式。首先，我们提出了一个解释，这意味着一个有限的子集的场是结构化的;我们通过一个数值参数，即零点来做到这一点。然后，我们将几个结果——特别是组合Nullstellensatz和系数定理——扩展到结构化网格上的多项式。主要的一点是，网格的结构允许对多项式的程度约束是放松的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Combinatorics, Probability & Computing 数学-计算机：理论方法

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： Published bimonthly, Combinatorics, Probability & Computing is devoted to the three areas of combinatorics, probability theory and theoretical computer science. Topics covered include classical and algebraic graph theory, extremal set theory, matroid theory, probabilistic methods and random combinatorial structures; combinatorial probability and limit theorems for random combinatorial structures; the theory of algorithms (including complexity theory), randomised algorithms, probabilistic analysis of algorithms, computational learning theory and optimisation.