Find a combinatorial generating subset of strata

Determine whether there is an interesting combinatorial choice of a subset of Richardson, positroid, or braid strata whose fundamental classes generate the Chow groups of the corresponding closed Richardson, projected Richardson, or brick varieties.

Background

The paper proves that the Chow groups of closed Richardson varieties, positroid varieties, and brick varieties are generated by the fundamental classes of their closed Richardson, positroid, or braid strata. However, these varieties may have substantially more strata than are needed to generate a given Chow or pure cohomology group; for example, the Grassmannian has one-dimensional second cohomology but can have many positroid divisors. The authors therefore leave unresolved the problem of identifying a smaller, combinatorially meaningful generating subset.