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}
}
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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