Paige Bright, Xinyu Fang, Barrett Heritage, Alex Iosevich, Tingsong Jiang, Hans Parshall, Maxwell Sun
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引用次数: 0
Abstract
In this paper, we generalize [6], [1], [5] and [3] by allowing the distance between two points in a finite field vector space to be defined by a general non-degenerate bilinear form or quadratic form. We prove the same bounds on the sizes of large subsets of for them to contain distance graphs with a given maximal vertex degree, under the more general notion of distance. We also prove the same results for embedding paths, trees and cycles in the general setting.
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.
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