Multidegrees of binomial edge ideals
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913347950084096 |
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| author | Cooper, Jacob Leventhal, Ethan |
| author_facet | Cooper, Jacob Leventhal, Ethan |
| contents | Let $G$ be a simple graph with binomial edge ideal $J_G$. We prove how to calculate the multidegree of $J_G$ based on combinatorial properties of $G$. In particular, we study the set $S_{\min}(G)$ defined as the collection of subsets of vertices whose prime ideals have minimum codimension. We provide results which assist in determining $S_{\min}(G)$, then calculate $S_{\min}(G)$ for star, horned complete, barbell, cycle, wheel, and friendship graphs, and use the main result of the paper to obtain the multidegrees of their binomial edge ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07365 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multidegrees of binomial edge ideals Cooper, Jacob Leventhal, Ethan Commutative Algebra Combinatorics 13H15, 05C25 (Primary) 05E40, 14C17 (Secondary) Let $G$ be a simple graph with binomial edge ideal $J_G$. We prove how to calculate the multidegree of $J_G$ based on combinatorial properties of $G$. In particular, we study the set $S_{\min}(G)$ defined as the collection of subsets of vertices whose prime ideals have minimum codimension. We provide results which assist in determining $S_{\min}(G)$, then calculate $S_{\min}(G)$ for star, horned complete, barbell, cycle, wheel, and friendship graphs, and use the main result of the paper to obtain the multidegrees of their binomial edge ideals. |
| title | Multidegrees of binomial edge ideals |
| topic | Commutative Algebra Combinatorics 13H15, 05C25 (Primary) 05E40, 14C17 (Secondary) |
| url | https://arxiv.org/abs/2405.07365 |