{"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/simplifying-modular-lattices-by-removing","title":"Simplifying modular lattices by removing doubly irreducible elements","arxiv_id":"2311.16643","date":"2023-11-28","proceeding":null,"authors":["Jukka Kohonen"],"abstract":"Lattices are simplified by removing some of their doubly irreducible elements, resulting in smaller lattices called racks. All vertically indecomposable modular racks of $n \\le 40$ elements are listed, and the numbers of all modular lattices of $n \\le 40$ elements are obtained by P\\'olya counting. SageMath code is provided that allows easy access both to the listed racks, and to the modular lattices that were not listed. More than 3000-fold savings in storage space are demonstrated.","url_abs":"https://arxiv.org/abs/2311.16643v2","url_pdf":"https://arxiv.org/pdf/2311.16643v2.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":"simplifying-modular-lattices-by-removing","repo_url":"https://bitbucket.org/jkohonen/modular-racks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}