On Rota's conjecture and excluded minors containing large projective geometries

We prove that an excluded minor for the class of GF(q)-representable matroids cannot contain a large projective geometry over GF(q) as a minor.

[1]  James G. Oxley,et al.  On Inequivalent Representations of Matroids over Finite Fields , 1996, J. Comb. Theory B.

[2]  R. Bixby.  A simple theorem on 3-connectivity , 1982 .

[3]  R. Brualdi.  Comments on bases in dependence structures , 1969, Bulletin of the Australian Mathematical Society.

[4]  Geoff Whittle,et al.  Stabilizers of Classes of Representable Matroids , 1999, J. Comb. Theory, Ser. B.

[5]  Stein Krogdahl.  The dependence graph for bases in matroids , 1977, Discret. Math..

[6]  Bert Gerards,et al.  The Excluded Minors for GF(4)-Representable Matroids , 1997, J. Comb. Theory, Ser. B.

[7]  W. T. Tutte.  Menger's theorem for matroids , 1965 .

[8]  Bert Gerards,et al.  Excluding a planar graph from GF(q)-representable matroids , 2007, J. Comb. Theory, Ser. B.

[9]  W. T. Tutte.  Connectivity in Matroids , 1966, Canadian Journal of Mathematics.

[10]  James G. Oxley,et al.  Matroid theory , 1992 .