Document Type : Original Manuscript


Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran.


Let $S=K[x_1,\ldots,x_n]$ be a polynomial ring over a field $K$ and
$I\subset S$ be a monomial ideal with a linear
resolution. Let
$\frak{m}=(x_1,\ldots,x_n)$ be the unique homogeneous maximal ideal and $I\frak{m}$ be a
polymatroidal ideal. We prove that if either $I\frak{m}$ is polymatroidal with strong
exchange property, or $I$ is a monomial ideal in at most 4
variables, then $I$ is polymatroidal. We also show that the first
homological shift ideal of polymatroidal ideal is again


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