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

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