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

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 is an element of {2, 3, 4}, the excluded minors for the class of Hi- representable matroids having at most 10 elements, and the excluded minors for the class of H5-representable matroids having at most 13 elements. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).