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Systems of parameters consisting of linear forms for monomial ideal quotients
Abstract
Let S=K[x1,…,xn] be a polynomial ring over a field K and let I be a monomial ideal of S. We classify linear systems of parameters of S/I over any field K using linear algebra and show explicit linear systems of parameters when K has at least n elements. If I(G) is the edge ideal of a perfect graph G, a cycle or the complement of a cycle, we show that S/I(G) has a 0-1 linear system of parameters, and for graphs with independence number equal to $2$, we characterize when S/I(G) has a 0-1 linear system of parameters.
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BibTeX
@misc{contreras2026systems,
title = {{Systems of parameters consisting of linear forms for monomial ideal quotients}},
author = {Edwin A. Contreras and Enrique Reyes and Rafael H. Villarreal},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30081},
eprint = {2609.30081},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30081},
}
RIS
TY - UNPB
TI - Systems of parameters consisting of linear forms for monomial ideal quotients
AU - Edwin A. Contreras
AU - Enrique Reyes
AU - Rafael H. Villarreal
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.30081
UR - https://arxiv.org/abs/2609.30081
AB - Let S=K[x_1,…,x_n] be a polynomial ring over a field K and let I be a monomial ideal of S. We classify linear systems of parameters of S/I over any field K using linear algebra and show explicit linear systems of parameters when K has at least n elements. If I(G) is the edge ideal of a perfect graph G, a cycle or the complement of a cycle, we show that S/I(G) has a 0-1 linear system of parameters, and for graphs with independence number equal to $2$, we characterize when S/I(G) has a 0-1 linear system of parameters.
ER -