Componentwise linearity of symbolic powers of polymatroidal ideals

Prove or disprove that every symbolic power I^(k) of every polymatroidal ideal I is componentwise linear for all integers k ≥ 1.

Background

Componentwise linearity requires each graded component of a homogeneous ideal to have a linear resolution. Based on computational evidence, the paper conjectures that symbolic powers of polymatroidal ideals possess this property uniformly in the symbolic-power index.

The paper verifies the conjecture for multiple subclasses and establishes linear quotients, which imply componentwise linearity, in several cases. The general assertion for arbitrary polymatroidal ideals is not settled by the results presented.