# Stabilizers of Classes of Representable Matroids

@article{Whittle1999StabilizersOC, title={Stabilizers of Classes of Representable Matroids}, author={G. 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 a… CONTINUE READING

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- 2010

- 27
- Highly Influenced
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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 22 REFERENCES

A Characterization of the Matroids Representable over GF(3) and the Rationals

- Mathematics, Computer Science
- 1995

- 42
- PDF

On Inequivalent Representations of Matroids over Finite Fields

- Mathematics, Computer Science
- 1996

- 59
- PDF