For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state a num- ber of conjectures that might be approachable using the structural characterization.
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Annals of Combinatorics
Networks and Optimization

Geelen, J., Gerards, B., & Whittle, G. (2015). The Highly Connected Matroids in Minor-closed Classes. Annals of Combinatorics, 19(1), 107–123. doi:10.1007/s00026-015-0251-3