Comparing Hilbert depth of $I$ with Hilbert depth of $S/I$. II

Andreea I. Bordianu; Mircea Cimpoeas

Comparing Hilbert depth of $I$ with Hilbert depth of $S/I$. II

Commutative Algebra 2024-04-09 v1 Combinatorics

Authors: Andreea I. Bordianu , Mircea Cimpoeas

Abstract

Let $I$ be a squarefree monomial ideal of $S=K[x_1,\ldots,x_n]$ . We prove that if $\operatorname{hdepth}(S/I)\leq 6$ of $n\leq 9$ then $\operatorname{hdepth}(I)\geq \operatorname{hdepth}(S/I)$ , giving a positive answer to a problem putted in arxiv:2403.17078

Keywords

Hilbert depth squarefree monomial ideal Stanley depth commutative algebra monomial ideal

Cite

@article{arxiv.2404.04646,
  title  = {Comparing Hilbert depth of $I$ with Hilbert depth of $S/I$. II},
  author = {Andreea I. Bordianu and Mircea Cimpoeas},
  journal= {arXiv preprint arXiv:2404.04646},
  year   = {2024}
}

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31 pages

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