{"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/when-can-you-tile-an-integer-rectangle-with","title":"When Can You Tile an Integer Rectangle with Integer Squares?","arxiv_id":"2308.15317","date":"2023-08-29","proceeding":null,"authors":["MIT CompGeom Group","Zachary Abel","Hugo A. Akitaya","Erik D. Demaine","Adam C. Hesterberg","Jayson Lynch"],"abstract":"This paper characterizes when an $m \\times n$ rectangle, where $m$ and $n$ are integers, can be tiled (exactly packed) by squares where each has an integer side length of at least 2. In particular, we prove that tiling is always possible when both $m$ and $n$ are sufficiently large (at least 10). When one dimension $m$ is small, the behavior is eventually periodic in $n$ with period 1, 2, or 3. When both dimensions $m,n$ are small, the behavior is determined computationally by an exhaustive search.","url_abs":"https://arxiv.org/abs/2308.15317v1","url_pdf":"https://arxiv.org/pdf/2308.15317v1.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":"when-can-you-tile-an-integer-rectangle-with","repo_url":"https://github.com/mit-compgeom/tiling-rectangles-with-squares","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}