Additivity of symmetric and subspace 2-designs

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-07-05 DOI:10.1007/s10623-024-01452-4

Marco Buratti, Anamari Nakić

引用次数: 0

Abstract

A 2-\((v,k,\lambda )\) design is additive (or strongly additive) if it is possible to embed it in a suitable abelian group G in such a way that its block set is contained in (or coincides with) the set of all zero-sum k-subsets of its point set. Explicit results on the additivity or strong additivity of symmetric designs and subspace 2-designs are presented. In particular, the strong additivity of PG\(_d(n,q)\), which was known to be additive only for \(q=2\) or \(d=n-1\), is always established.

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对称和子空间 2 设计的可加性

如果可以将一个 2-（(v,k,\lambda )\）设计嵌入到一个合适的无方群 G 中，使得其块集包含在（或重合于）其点集的所有零和 k 子集的集合中，那么这个设计就是可加的（或强可加的）。本文给出了对称设计和子空间 2 设计的可加性或强可加性的明确结果。特别是，PG（_d(n,q)\）的强可加性总是成立的，而已知的可加性只适用于\(q=2\)或\(d=n-1\)。

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.

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