Extremal matroid classes

Identify classes of matroids that are extremal.

Background

The authors state that a complete characterization of all extremal matroids appears out of reach and instead invite the identification of substantial or structurally meaningful classes. Such classes would provide systematic sources of vertices of the polytope Ωr,n\Omega_{r,n} and could help test non-negativity conjectures for valuative invariants.

References

Although a characterization of all extremal matroids seems out of reach, we feel motivated to invite the reader to find more meaningful classes: Identify classes of matroids that are extremal.

— The polytope of all matroids  (2502.20157 - Ferroni et al., 27 Feb 2025) in Section 6.1, “Extremal matroids and the pursuit of counterexamples in matroid theory”