Normality and unimodular triangulations of random delta-matroid polytopes

Determine whether the proportion of labeled delta-matroids on [n] whose delta-matroid polytopes are normal tends to zero as n tends to infinity, and whether the proportion whose delta-matroid polytopes have unimodular triangulations also tends to zero.

Background

The paper constructs a spanning delta-matroid polytope that is not normal, showing that normality results for matroid base polytopes do not extend to delta-matroids. The problem asks whether nonnormality, and even failure of unimodular triangulability, is asymptotically typical among labeled delta-matroids.

References

Does \frac{|{D\in\mathfrak D_n:P(D)\text{ is normal}}|} {|\mathfrak D_n|}\longrightarrow0? At least, does \frac{|{D\in\mathfrak D_n:P(D)\text{ has a unimodular triangulation}}|} {|\mathfrak D_n|}\longrightarrow0?

— Most $(0,1)$-polytopes are not normal  (2609.02778 - Morales, 2 Sep 2026) in Problem delta-matroid polytopes, Section 5, Open problems