Extension to polymatroids and megamatroids

Construct an extension of the chromatic word-quasisymmetric functions of matroids to polymatroids and megamatroids.

Background

The paper uses results of Derksen and Fink concerning valuative functions on polymatroids and megamatroids. Those results imply that analogous lower-bound questions are immediately available in these broader settings.

The authors leave unresolved how the matroidal definition based on generic weight functions and normal fans should be extended to polymatroids and megamatroids.