Polytope associated with the chromatic valuative function

Determine the polytope corresponding to the valuative function \(\ncPsi\) of chromatic word-quasisymmetric functions, and likewise the corresponding polytope for the chromatic quasisymmetric function \(\cPsi\).

Background

The paper discusses polytopes associated with valuative functions as projections of the polytope of all matroids. The latter is described using coefficients in expansions of matroid base-polytope indicators in terms of nested matroid indicators.

The authors ask for the specific polytope obtained from the chromatic word-quasisymmetric valuation introduced in the paper, together with its commutative counterpart.