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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.09153 |
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| _version_ | 1866917328012181504 |
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| author | Li, Zhenzhi Shen, Wujie |
| author_facet | Li, Zhenzhi Shen, Wujie |
| contents | We study the structure of the space $Ω_3(G)$ of $\partial$-invariant 3-paths in a directed graph $G$. We prove that $Ω_3(G)$ admits a basis consisting of trapezohedral paths $τ_m$ ($m \ge 2$) and their merging images. Moreover, we provide an explicit construction of such a basis and, as a consequence, obtain an algorithm with time complexity $O(|V(G)|^5)$ for computing the dimension and a basis of $Ω_3(G)$ for any finite digraph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09153 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $\partial$-invariant path generators for digraphs Li, Zhenzhi Shen, Wujie Combinatorics We study the structure of the space $Ω_3(G)$ of $\partial$-invariant 3-paths in a directed graph $G$. We prove that $Ω_3(G)$ admits a basis consisting of trapezohedral paths $τ_m$ ($m \ge 2$) and their merging images. Moreover, we provide an explicit construction of such a basis and, as a consequence, obtain an algorithm with time complexity $O(|V(G)|^5)$ for computing the dimension and a basis of $Ω_3(G)$ for any finite digraph. |
| title | $\partial$-invariant path generators for digraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.09153 |