The Templates for Some Classes of Quaternary Matroids

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.

arXiv comment83 pages; minor corrections in Version 4; accepted for publication by Journal of Combinatorial Theory, Series B

References in corpus (5)

• Confinement of matroid representations to subsets of partial fields
• Lifts of matroid representations over partial fields
• Templates for Binary Matroids
• On perturbations of highly connected dyadic matroids
• The highly connected even-cycle and even-cut matroids

Cited by in corpus (1)

• On the Highly Connected Dyadic, Near-Regular, and Sixth-Root-of-Unity Matroids