{"paper":{"title":"The tilings of deficient squares by ribbon L-tetrominoes are diagonally cracked","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Viorel Nitica","submitted_at":"2017-01-02T15:28:39Z","abstract_excerpt":"We consider tilings of deficient rectangles by the set $\\mathcal{T}_4$ of ribbon $L$-tetrominoes. A tiling exists iff the rectangle is a square of odd side. The missing cell is on the main NW--SE diagonal, in an odd position if the square is $(4m+1)\\times (4m+1)$ and in an even position for $(4m+3)\\times (4m+3)$. The majority of the tiles in a tiling are paired and each pair tiles a $2\\times 4$ rectangle. The tiles in an irregular position and the missing cell form a NW--SE diagonal crack, located in a thin region symmetric about the diagonal, made out of $3\\times 3$ squares that overlap over "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00419","kind":"arxiv","version":2},"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"}