{"paper":{"title":"A rigidity property of ribbon L-shaped n-ominoes and generalizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Viorel Nitica","submitted_at":"2014-06-03T19:31:51Z","abstract_excerpt":"Let n integer greater or equal to 4 and even and let T_n be the set of ribbon L-shaped n-ominoes. We study tiling problems for regions in a square lattice by T_n. Our main result shows a remarkable rigidity property: a tiling of the first quadrant by T_n is possible if and only if it reduces to a tiling by 2 x n and n x 2 rectangles. An application is the classification of all rectangles that can be tiled by T_n: a rectangle can be tiled by T_n if and only if both of its sides are even and at least one side is divisible by n. Another application is the existence of the local move property for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0823","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":""},"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"}