Squarefree powers of closed neighborhood ideals
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918391331160064 |
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| author | Nambi, Marie Amalore Qureshi, Ayesha Asloob |
| author_facet | Nambi, Marie Amalore Qureshi, Ayesha Asloob |
| contents | 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 $ν$-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 $ν$-th squarefree power of the closed neighborhood ideal of caterpillar graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_15229 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Squarefree powers of closed neighborhood ideals Nambi, Marie Amalore Qureshi, Ayesha Asloob Commutative Algebra Combinatorics 13D02, 05E40, 05E45, 05C70 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 $ν$-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 $ν$-th squarefree power of the closed neighborhood ideal of caterpillar graphs. |
| title | Squarefree powers of closed neighborhood ideals |
| topic | Commutative Algebra Combinatorics 13D02, 05E40, 05E45, 05C70 |
| url | https://arxiv.org/abs/2603.15229 |