On the Hilbert depth of a special class of squarefree monomial ideals

Andreea I. Bordianu; Mircea Cimpoeas

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arXiv · 2607.11691

On the Hilbert depth of a special class of squarefree monomial ideals

Andreea I. Bordianu·Mircea Cimpoeas

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Abstract

Let $r$ and $n$ be two positive integers and $S=K[x_1,\ldots,x_{n+r-1}]$, the ring of polynomials in $n+r-1$ variable, over a field $K$. We consider the squarefree monomial ideal $I_{n,r}:= x_1 \cdots x_{r-1} (x_{r},\ldots,x_{r+n-1}) \subset S$ and we prove several results regarding the Hilbert depth of $S/I_{n,r}$. Also, we consider the special case $n=r$.

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Andreea I. Bordianu, Mircea Cimpoeas. 2026-07-13. On the Hilbert depth of a special class of squarefree monomial ideals. https://arxiv.org/abs/2607.11691

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