Extend characteristic-polynomial properties to rational q-polymatroids

Determine whether properties of the characteristic polynomial of a $(q,r)$-polymatroid involving independent spaces, circuits, and flats can be generalized to the corresponding structures of rational q-polymatroids.

Background

The paper introduces the characteristic Puiseux polynomial for rational q-polymatroids and observes that results based solely on lattice-theoretic concepts extend naturally from $(q,r)$-polymatroids. In contrast, properties involving independent spaces, dependent spaces, circuits, and related q-polymatroid structures require new arguments. The authors explicitly state that it is currently unknown whether these results can be transferred to rational q-polymatroids.