{"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/t-tetrominos-in-arithmetic-progression","title":"T-Tetrominos in Arithmetic Progression","arxiv_id":"2207.00533","date":"2022-07-01","proceeding":null,"authors":["Emily Feller","Robert Hochberg"],"abstract":"A famous result of D. Walkup is that an $m\\times n$ rectangle may be tiled by T-tetrominos if and only if both $m$ and $n$ are multiples of 4. The \"if\" portion may be proved by tiling a $4\\times 4$ block, and then copying that block to fill the rectangle; but, this leads to regular, periodic tilings. In this paper we investigate how much \"order\" must be present in every tiling of a rectangle by T-tetrominos, where we measure order by length of arithmetic progressions of tiles.","url_abs":"https://arxiv.org/abs/2207.00533v2","url_pdf":"https://arxiv.org/pdf/2207.00533v2.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":"t-tetrominos-in-arithmetic-progression","repo_url":"https://github.com/roberthochberg/fellerhochberg","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}