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arXiv · 2603.15229

Squarefree powers of closed neighborhood ideals

Marie Amalore Nambi·Ayesha Asloob Qureshi
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Abstract

In this article, we characterize all trees whose highest non-vanishing squarefree power of the closed neighborhood ideal is componentwise linear. In addition, we investigate the Castelnuovo-Mumford regularity of the $\nu$-th squarefree power of the closed neighborhood ideal of trees and show that this number can be arbitrarily larger than the degree of the ideal. Finally, we give a formula for the regularity of $\nu$-th squarefree power of the closed neighborhood ideal of caterpillar graphs.

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Marie Amalore Nambi, Ayesha Asloob Qureshi. 2026-03-16. Squarefree powers of closed neighborhood ideals. https://arxiv.org/abs/2603.15229

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