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

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.

arXiv comment36 pages including 11-page appendix, 2 figures

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