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arXiv · 2307.14614

The excluded minors for GF(5)-representable matroids on ten elements

Nick Brettell
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Abstract

Mayhew and Royle (2008) showed that there are 564 excluded minors for the class of GF(5)-representable matroids having at most 9 elements. We enumerate the excluded minors for GF(5)-representable matroids having 10 elements: there are precisely 2128 such excluded minors. In the process we find, for each $i \in \{2,3,4\}$, the excluded minors for the class of $\mathbb{H}_i$-representable matroids having at most 10 elements, and the excluded minors for the class of $\mathbb{H}_5$-representable matroids having at most 13 elements.

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Nick Brettell. 2024-10-08. The excluded minors for GF(5)-representable matroids on ten elements. https://doi.org/10.1016/j.aam.2025.102864

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