The Density Hales-Jewett Theorem and matroid theory
|Affiliation:||Victoria University of Wellington|
|Room:||Mathematics & Computer Building (MC) 5158|
The Density Hales-Jewett theorem is a powerful tool in Ramsey theory that finds a highly structured subset in an arbitrary dense set of strings over a finite alphabet. A direct consequence for matroids is that any dense GF(q)-representable matroid of huge rank contains a large restriction isomorphic to an affine geometry over GF(q). I will show that the same statement holds for matroids in any fixed minor-closed class that grows at similar rate to the class of GF(q)-representable matroids, and discuss some related results and conjectures. This is joint work with Jim Geelen.
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