For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state a num- ber of conjectures that might be approachable using the structural characterization.
matroids, minors, connectivity, girth, linear codes, ML threshold function, growth rate
Matroids, geometric lattices (msc 05B35)
Other (theme 6)
Birkhäuser
dx.doi.org/10.1007/s00026-015-0251-3
Annals of Combinatorics
Networks and Optimization

Geelen, J, Gerards, A.M.H, & Whittle, G. (2015). The Highly Connected Matroids in Minor-closed Classes. Annals of Combinatorics, 19(1), 107–123. doi:10.1007/s00026-015-0251-3