Depth of the 3-path Ideal of Square of a Path
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866916838881886208 |
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| author | Yang, Liuqing Chu, Lizhong |
| author_facet | Yang, Liuqing Chu, Lizhong |
| contents | In this note, we compute depth of the 3-path ideal of square of a path and show that the 3-path ideal I3(P 2
n) of square of a path graph is Cohen-Macaulay if and only if n = 3 or 4. Also, we consider the limit behavior of depth of powers of the 3-path ideal of square of a path. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Depth of the 3-path Ideal of Square of a Path Yang, Liuqing Chu, Lizhong Commutative Algebra In this note, we compute depth of the 3-path ideal of square of a path and show that the 3-path ideal I3(P 2 n) of square of a path graph is Cohen-Macaulay if and only if n = 3 or 4. Also, we consider the limit behavior of depth of powers of the 3-path ideal of square of a path. |
| title | Depth of the 3-path Ideal of Square of a Path |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2507.08516 |