{"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/there-is-no-perfect-mondrian-partition-for","title":"There is no perfect Mondrian partition for squares of side lengths less than 1001","arxiv_id":"2311.02385","date":"2023-11-04","proceeding":null,"authors":["Natalia García-Colín","Dimitri Leemans","Mia Müßig","Érika Roldán"],"abstract":"In mathematics, a dissection of a square (or rectangle) into non-congruent rectangles is a Mondrian partition. If all the rectangles have the same area, it is called a perfect Mondrian partition. In this paper, we present a computational result by which we can affirm that there is no perfect Mondrian partition of a length $n$ square for $n\\leq 1000$. Using the same algorithm we have been able to establish that there is no perfect Mondrian partition of a $n \\times m$ rectangle for $n,m \\leq 400$.","url_abs":"https://arxiv.org/abs/2311.02385v1","url_pdf":"https://arxiv.org/pdf/2311.02385v1.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":"there-is-no-perfect-mondrian-partition-for","repo_url":"https://github.com/phoenixsmaug/mondrian","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}