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arXiv · 2605.13617

On Some Properties of LCM-Lattices of Edge Ideals of k-Uniform Hypergraphs

Muneeba Mansha·Sarfraz Ahmad
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Abstract

In this article, we investigate the combinatorial and algebraic properties of the lcm-lattice associated with the edge ideal of a hypergraph. Let $\H$ be a hypergraph, $I(\H)$ its corresponding edge ideal in a polynomial ring in $n$ variables, and $\mathrm{Icm}(I(\H))$ the associated lcm-lattice. We establish conditions under which the lcm-lattice of an edge ideal is Boolean, modular, or complemented. Furthermore, we extend these results to the case of the product of lcm-lattices in the complemented case. Additionally, we study the effects of polarization on the lcm-lattices of $I(\H)$ and its polarized ideal.

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Muneeba Mansha, Sarfraz Ahmad. 2026-05-13. On Some Properties of LCM-Lattices of Edge Ideals of k-Uniform Hypergraphs. https://arxiv.org/abs/2605.13617

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