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Information Journal Paper

Title

POLYMATROIDAL IDEALS AND LINEAR RESOLUTION

Pages

  147-153

Abstract

 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 linearresolution. Let$\frak{m}=(x_1,\ldots,x_n)$ be the unique homogeneous maximal ideal and $I\frak{m}$ be apolymatroidal ideal. We prove that if either $I\frak{m}$ is polymatroidal with strongexchange property, or $I$ is a monomial ideal in at most 4variables, then $I$ is polymatroidal. We also show that the firsthomological shift ideal of polymatroidal ideal is againpolymatroidal.

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