A class of functions and their application in constructing semisymmetric designs

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-20 DOI:10.1007/s10623-024-01455-1

Robert S. Coulter, Bradley Fain

引用次数: 0

Abstract

We introduce the notion of a semiplanar function of index \(\lambda \), generalising several previous concepts. We show how semiplanar functions can be used to construct semisymmetric designs using an incidence structure determined by the function. Issues regarding the connectivity of the structure are then considered. The question of existence is addressed by establishing monomial examples over finite fields, and we examine how composition with linearized polynomials can lead to further classes of examples. We end by returning to the incidence structure and considering maximal intersection sets when the incidence structure is constructed using a particular class of functions.

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一类函数及其在构建半对称设计中的应用

我们引入了指数为 \(\lambda \)的半平面函数的概念，概括了之前的几个概念。我们展示了如何利用半平面函数来构造由函数决定的入射结构的半对称性设计。然后，我们考虑了有关结构连接性的问题。通过建立有限域上的单项式范例，我们解决了存在性问题，并研究了线性化多项式的组合如何带来更多范例。最后，我们将回到入射结构，并考虑当入射结构使用某一类函数构建时的最大交集。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.