Bandari–Herzog's conjecture on componentwise polymatroidal ideals

Let $S=K[x_1,\dots,x_n]$ be a polynomial ring over a field $K$. A monomial ideal $I\subset S$ is componentwise polymatroidal when each component $I_{\langle j\rangle}$ is polymatroidal, where $I_{\langle j\rangle}$ is generated by the degree-$j$ monomials belonging to $I$. Bandari–Herzog's conjecture. If $I$ is componentwise polymatroidal, then $I$ has linear quotients. Since polymatroidal ideals have linear quotients, this is a particular case of Jahan–Zheng's conjecture; the source presents it as the conjecture proved positively by the paper.