切换图与设计
Switching graphs and designs
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中文总结 AI 辅助
本文推广切换方法至可除设计，证明图与设计切换方法的等价性，并由此得到构造2-设计的新方法。
中文摘要 AI 辅助
切换方法可视为某些不改变组合结构基本参数的局部变换。文献中已有大量工作致力于关联和统一编码与设计、以及阿达玛矩阵与图的切换理论。本文所考虑的组合结构为图与设计。我们将已知的用于构造2-设计的切换方法推广到可除设计，并给出其应用的一些实例。此外，我们证明了图的切换方法与设计的切换方法之间的若干等价性，并作为副产品，获得了一种新的构造2-设计的切换方法。
英文摘要
Switching methods can be seen as certain local transformations that do not alter their basic parameters of a combinatorial structure. Efforts have been devoted in the literature to relate and unify the switching theories for codes and designs, and also for Hadamard matrices and graphs. The combinatorial structures we consider in this paper are graphs and designs. We show an extension of known switching method for constructing 2-designs to divisible designs, and then provide some examples of its application. Moreover, we prove several equivalences between switching methods for graphs and designs, and as a byproduct, we obtain a new switching method to obtain 2-designs.
发表机构
- Eindhoven University of Technology（埃因霍温理工大学）
- Vrije Universiteit Brussel（布鲁塞尔自由大学）
- University of Rijeka（里耶卡大学）
- Ghent University（根特大学）
机构由 AI 辅助整理，请以论文原文为准。
