H*-polynomials of other Cayley polytopes

Determine whether the Ehrhart-series technique used to identify the support-enumerator of the draconian sequences D(G) with the h*-polynomial of the corresponding root polytope can yield simple calculations of h*-polynomials for other Cayley polytopes.

Background

The paper relates Minkowski sums of simplices to root polytopes by interpreting the relevant support-enumerator as an h*-polynomial through a direct manipulation of the Ehrhart series. A Cayley polytope generalizes this construction from simplices to arbitrary polytopes P_1, ..., P_m in Rn.

The open problem asks whether the same type of generating-function argument can provide comparably simple h*-polynomial computations for classes of Cayley polytopes beyond those arising from simplices and bipartite graphs.

References

Can this technique be used to give a simple calculation of the $h*$-polynomials of some other Cayley polytopes?

— Counting Lattice Points in Minkowski Sums of Cross Polytopes  (2608.16037 - Wang et al., 17 Aug 2026) in Section 4, Further Questions, first Problem

Can their results be extended to the entire family? Can we generalize the technique for computing the $h*$-polynomials of Minkowski sums of cross polytopes? Additionally, for which instances do these $h*$-polynomials admit especially simple or explicit formulas?

— Counting Lattice Points in Minkowski Sums of Cross Polytopes  (2608.16037 - Wang et al., 17 Aug 2026) in Section 4, Further Questions, second Problem