Koszulness of polymatroid base rings

Determine whether the toric ring of every polymatroid base polytope that has a flag unimodular triangulation is Koszul, including whether the toric ring of the Fano matroid is Koszul.

Background

The paper recalls Herzog and Hibi’s question concerning Koszulness for polymatroid base rings. The question is especially relevant because flag unimodular triangulations do not imply Koszulness for arbitrary (0,1)-polytopes, while polymatroid base polytopes may possess additional structure. The Fano matroid is identified as a specific test case.

References

Is every polymatroid base ring Koszul?

— Most $(0,1)$-polytopes are not normal  (2609.02778 - Morales, 2 Sep 2026) in Problem Herzog--Hibi, Section 1, Introduction