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1. Verfasser:	Ghasr, Fahimeh Khosh-Ahang
Format:	Preprint
Veröffentlicht:	2025
Schlagworte:	Commutative Algebra Combinatorics 05E45, 11C20, 13P10
Online-Zugang:	https://arxiv.org/abs/2510.06729
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author	Ghasr, Fahimeh Khosh-Ahang
author_facet	Ghasr, Fahimeh Khosh-Ahang
contents	We provide necessary and sufficient conditions for simplicial complexes whose determinantal facet ideals admit reduced Grobner bases under diagonal term orders. Building on and extending foundational results for binomial edge ideals and determinantal ideals, we introduce two new classes of simplicial complexes-strong closed and poor closed-that generalize the notion of closedness in higher dimensions. Our main theorem offers a unified framework that recovers and refines several known results, including those for unit interval graphs and determinantal ideals of complete graphs. In particular, we correct and generalize prior characterizations of Grobner bases for determinantal facet ideals, establishing radicality for strong closed complexes and providing a new proof for the Grobner basis of maximal minors.
format	Preprint
id	arxiv_https___arxiv_org_abs_2510_06729
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Grobner bases for determinantal facet ideals of simplicial complexes Ghasr, Fahimeh Khosh-Ahang Commutative Algebra Combinatorics 05E45, 11C20, 13P10 We provide necessary and sufficient conditions for simplicial complexes whose determinantal facet ideals admit reduced Grobner bases under diagonal term orders. Building on and extending foundational results for binomial edge ideals and determinantal ideals, we introduce two new classes of simplicial complexes-strong closed and poor closed-that generalize the notion of closedness in higher dimensions. Our main theorem offers a unified framework that recovers and refines several known results, including those for unit interval graphs and determinantal ideals of complete graphs. In particular, we correct and generalize prior characterizations of Grobner bases for determinantal facet ideals, establishing radicality for strong closed complexes and providing a new proof for the Grobner basis of maximal minors.
title	Grobner bases for determinantal facet ideals of simplicial complexes
topic	Commutative Algebra Combinatorics 05E45, 11C20, 13P10
url	https://arxiv.org/abs/2510.06729

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