Title: Circuit-hyperplane relaxation and matroid representation
|Affiliation:||University of Waterloo|
Relaxing a circuit-hyperplane in a representable matroid can destroy representability. Indeed, both the non-Pappus matroid and the V\’ amos matroid are obtained by relaxing a circuit-hyperplane in a representable matroid.
We characterize the GF(4)-representable matroids that have a circuit-hyperplane whose relaxation is also GF(4)-representable.
We hope to use the same techniques for GF(5)-representability, which will hopefully lead to the excluded-minor characterization for the class of GF(5)-representable matroids. This is joint work with Rutger Campbell and Geoff Whittle.
Parts of the talk will require some understanding of matroid theory, but our main question can be stated in terms of matrices, and significant parts of the talk will be accessible to people who have no prior exposure to matroids.
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