# The Templates for Some Classes of Quaternary Matroids

## TL;DR

This paper characterizes highly connected members of certain quaternary matroid classes, using frame templates to determine extremal functions and deepen understanding of their structure.

## Contribution

It introduces a comprehensive characterization of highly connected quaternary matroids and explores frame templates as a key tool for structural analysis.

## Key findings

- Complete characterization of highly connected golden-mean matroids
- Determination of extremal functions for these classes
- In-depth study of frame templates

## Abstract

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.