Subject to hypotheses based on the matroid structure theory of Geelen, Gerards, and Whittle, we completely characterize the highly connected members of the class of golden-mean matroids and several other closely related classes of quaternary matroids. This leads to a determination of the eventual extremal functions for these classes. One of the main tools for obtaining these results is the notion of a frame template. Consequently, we also study frame templates in significant depth.

中文翻译：

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某些四级拟阵的模板

根据基于Geelen，Gerards和Whittle拟阵结构理论的假设，我们完全表征了均值类拟阵和其他几个紧密相关的第四类拟阵的高度关联成员。这导致确定这些类别的最终极值功能。获得这些结果的主要工具之一是框架模板的概念。因此，我们还将深入研究框架模板。