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Description: |
It was recently proven (J. Geelen, B. Gerards, G. Whittle) that linear dependence over any given finite field can be characterized combinatorically, via matroids, in terms of a finite number of excluded subconfigurations (minors). It is known that representability over the reals can not be characterized conviniently in terms of excluded minors.
In this talk we discuss some of the results obtained in an approach, via oriented matroids, to a combinatorial characterization of linear dependencies of 0-1-vectors over the reals.
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