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arXiv · 2306.11015

On the Hilbert depth of certain monomial ideals and applications

Silviu Balanescu·Mircea Cimpoeas
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Abstract

We study the Stanley depth and the Hilbert depth for $I$ and $S/I$, where $I\subset S=K[x_1,\ldots,x_N]$ is the intersection of monomial prime ideals with disjoint sets of variables. As an application, we obtain bounds for the Stanley depth of $I_{n,m}^t$ and $J_{n,m}^t$, where $I_{n,m}$ is the $m$-path ideal of the path graph of length $n$ and $J_{n,m}$ is the the $m$-path ideal of the cycle graph of length $n$.

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Silviu Balanescu, Mircea Cimpoeas. 2023-06-19. On the Hilbert depth of certain monomial ideals and applications. https://arxiv.org/abs/2306.11015

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