{"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/representations-of-torsion-free-arithmetic","title":"Representations of torsion-free arithmetic matroids","arxiv_id":"1908.04137","date":"2019-08-12","proceeding":null,"authors":["Roberto Pagaria","Giovanni Paolini"],"abstract":"We study the representability problem for torsion-free arithmetic matroids. By using a new operation called \"reduction\" and a \"signed Hermite normal form\", we provide and implement an algorithm to compute all the representations, up to equivalence. As an application, we disprove two conjectures about the poset of layers and the independence poset of a toric arrangement.","url_abs":"http://arxiv.org/abs/1908.04137v1","url_pdf":"http://arxiv.org/pdf/1908.04137v1.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":"representations-of-torsion-free-arithmetic","repo_url":"https://github.com/giove91/arithmat","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}