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On the Hilbert depth of a special class of squarefree monomial ideals
Abstract
Let r and n be two positive integers and S=K[x1,…,xn+r−1], the ring of polynomials in n+r−1 variable, over a field K. We consider the squarefree monomial ideal In,r:= x1 ⋯ xr−1 (xr,…,xr+n−1) ⊂ S and we prove several results regarding the Hilbert depth of S/In,r. Also, we consider the special case n=r.
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BibTeX
@misc{bordianu2026hilbert,
title = {{On the Hilbert depth of a special class of squarefree monomial ideals}},
author = {Andreea I. Bordianu and Mircea Cimpoeas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.11691},
eprint = {2607.11691},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.11691},
}
RIS
TY - UNPB
TI - On the Hilbert depth of a special class of squarefree monomial ideals
AU - Andreea I. Bordianu
AU - Mircea Cimpoeas
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2607.11691
UR - https://arxiv.org/abs/2607.11691
AB - Let r and n be two positive integers and S=K[x_1,…,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 ⋯ x_r−1 (x_r,…,x_r+n−1) ⊂ S and we prove several results regarding the Hilbert depth of S/I_n,r. Also, we consider the special case n=r.
ER -