{"paper":{"title":"Automatic Enumeration of Tilings by Polyominoes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lucy Martinez","submitted_at":"2026-07-31T12:52:59Z","abstract_excerpt":"We revisit Zeilberger's computational framework for enumerating polyomino tilings and demonstrate its use in counting tilings of $k\\times n$ boards by $L$-tetrominoes, allowing rotations. Recently, B\\v{e}lohoubek and Slav\\'ik gave a generating function for tilings of $2n\\times 4$ boards by $L$-tetrominoes. Motivated by their work, we first verify the method by automatically recovering their generating function. We then apply the method to widths $5$ through $9$ and obtain explicit rational generating functions and new integer sequences that are not currently listed in the OEIS."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29369","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.29369/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}