{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/multidegrees-of-binomial-edge-ideals","title":"Multidegrees of binomial edge ideals","arxiv_id":"2405.07365","date":"2024-05-12","proceeding":null,"authors":["Jacob Cooper","Ethan Leventhal"],"abstract":"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.","url_abs":"https://arxiv.org/abs/2405.07365v1","url_pdf":"https://arxiv.org/pdf/2405.07365v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"multidegrees-of-binomial-edge-ideals","repo_url":"https://github.com/MrBobJrIV/Multidegrees-of-Binomial-Edge-Ideals","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}