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We know the excluded minors for the matroids representable over GF(2), GF(3) and GF(4). What are the chances of explicitly finding the excluded minors for matroids representable over GF(5)?
We have an excellent understanding of the classes that arise when we consider matroids representable over GF(2) and other fields. We also have an algebraic understanding of the classes that arise for matroids representable over GF(3) and other fields. What are the chances of describing the classes for GF(4) and other fields?
Recent explicit descriptions of the excluded minors for the class of 2-regular matroids and 3-regular matroids (almost) can be thought of as baby steps towards the resolution of the questions posed above. But let's be real, is there genuine hope?
