Möbius support of a polymatroid is a generalized polymatroid

Ascertain whether, for any polymatroid P on [p], the Möbius support (P) = { n ∈ N^p | μ_P(n) ≠ 0 }, where μ_P is defined inductively on the independence polytope I(P), forms a generalized polymatroid, meaning that homogenization of its support yields a polymatroid.

Background

For a polymatroid P, the Möbius function μ_P is defined on Z^p using the independence polytope I(P), and the Möbius support (P) collects those lattice points with μ_P ≠ 0. A generalized polymatroid is a set whose homogenized support is a polymatroid.

This conjecture, attributed to Castillo, Cid-Ruiz, Mohammadi, and Montaño, had been proved previously when P is realizable and when P is a matroid. The paper states it settles the conjecture generally by showing the Möbius support is indeed a generalized polymatroid.