Upper bounds for the Stanley depth

Muhammad Ishaq

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arXiv · 1003.3471

Upper bounds for the Stanley depth

Muhammad Ishaq

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Abstract

Let $I\subset J$ be monomial ideals of a polynomial algebra $S$ over a field. Then the Stanley depth of $J/I$ is smaller or equal with the Stanley depth of $\sqrt{J}/\sqrt{I}$. We give also an upper bound for the Stanley depth of the intersection of two primary monomial ideals $Q$, $Q'$, which is reached if $Q$, $Q'$ are irreducible, ht$(Q+Q')$ is odd and $\sqrt{Q}$, $\sqrt{Q'}$ have no common variable.

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Muhammad Ishaq. 2010-03-17. Upper bounds for the Stanley depth. https://arxiv.org/abs/1003.3471

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