On the Hilbert depth of certain monomial ideals and applications
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917715785023488 |
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| author | Balanescu, Silviu Cimpoeas, Mircea |
| author_facet | Balanescu, Silviu Cimpoeas, Mircea |
| contents | 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 $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11015 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Hilbert depth of certain monomial ideals and applications Balanescu, Silviu Cimpoeas, Mircea Commutative Algebra Combinatorics 05A18, 06A07, 13C15, 13P10, 13F20 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 $n$. |
| title | On the Hilbert depth of certain monomial ideals and applications |
| topic | Commutative Algebra Combinatorics 05A18, 06A07, 13C15, 13P10, 13F20 |
| url | https://arxiv.org/abs/2306.11015 |