Nullities of multisets and value sets of multivariate polynomials

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-07-23 DOI:10.1016/j.ffa.2025.102709

Wei Cao

引用次数: 0

Abstract

We extend the nullity for a finite 1-tuple multiset, which was introduced by Nica, to a finite m-tuple multiset, and then use it to give an upper bound for the value set of a multivariate polynomial over the multisets drawn from a field. Our results generalize and refine two generalizations of original Wan's upper bound for the value set of a univariate polynomial in finite fields.

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多元多项式的多集和值集的零值

本文将Nica提出的有限一元元组多集的零性推广到有限一元元组多集，并利用它给出了由域绘制的多集上的多元多项式的值集的上界。我们的结果推广和改进了有限域中单变量多项式值集的原始Wan上界的两个推广。

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

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.