Möbius support is a generalized polymatroid

Establish whether the Möbius support of a polymatroid P, defined as the set {n ∈ N^p | μ_P(n) ≠ 0} where μ_P is the Möbius function determined recursively on the independence polytope I(P), is a generalized polymatroid (i.e., its homogenization yields a polymatroid).

Background

The Möbius function μ_P is defined on the independence polytope I(P) and its support (the set of integer points where μ_P is nonzero) encodes combinatorial information about P. Prior results established the conjecture for realizable polymatroids and for matroids, motivating the general formulation.

This paper introduces the cave polynomial and shows it equals the generating function of μ_P, which is used to argue structural properties of the Möbius support. The conjecture is stated explicitly before later being claimed resolved within the paper.