Symbolic-power regularity and componentwise linearity for ideals with linear powers

Determine whether every equigenerated monomial ideal I whose ordinary powers all have linear resolutions or linear quotients satisfies reg I^(k) = reg I^k and has symbolic powers I^(k) that are componentwise linear or have linear quotients for all integers k ≥ 1.

Background

Question D extends the paper’s conjectures beyond polymatroidal ideals to equigenerated monomial ideals whose ordinary powers have linear resolutions or linear quotients. It asks simultaneously for equality of the regularities of symbolic and ordinary powers and for componentwise linearity or linear quotients of every symbolic power.

The question is motivated by results cited in the paper concerning ideals with linear powers and by the families established in the paper itself. It is posed as an unresolved generalization rather than proved in the paper.