polymatroidal ideals and linear resolution

Let $s=k[x_1,ldots,x_n]$ be a polynomial ring over a field $k$ and $frak{m}=(x_1,ldots,x_n)$ be the unique homogeneous maximal ideal. ##let $isubset s$ be a monomial ideal with a linear resolution and $ifrak{m}$ be a polymatroidal ideal. ##we prove that if either $ifrak{m}$ is polymatroidal with strong exchange property, or $i$ is a monomial ideal in at most 4 variables, then $i$ is polymatroidal