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# Stabilizers of Classes of Representable Matroids

@article{Whittle1999StabilizersOC, title={Stabilizers of Classes of Representable Matroids}, author={Geoff Whittle}, journal={J. Comb. Theory, Ser. B}, year={1999}, volume={77}, pages={39-72} }

- Published 1999 in J. Comb. Theory, Ser. B
DOI:10.1006/jctb.1999.1908

Let M be a class of matroids representable over a field F. A matroid N # M stabilizes M if, for any 3-connected matroid M # M, an F-representation of M is uniquely determined by a representation of any one of its N-minors. One of the main theorems of this paper proves that if M is minor-closed and closed under duals, and N is 3-connected, then to show that N is a stabilizer it suffices to check 3-connected matroids in M that are single-element extensions or coextensions of N, or are obtained by… CONTINUE READING

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