{"paper":{"title":"Signed tilings by ribbon L n-ominoes, n even, via Groebner bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Kenneth Gill, Viorel Nitica","submitted_at":"2016-01-04T17:07:10Z","abstract_excerpt":"Let $\\mathcal{T}_n$ be the set of ribbon $L$-shaped $n$-ominoes for some $n\\ge 4$ even, and let $\\mathcal{T}_n^+$ be $\\mathcal{T}_n$ with an extra $2\\times 2$ square. We investigate signed tilings of rectangles by $\\mathcal{T}_n$ and $\\mathcal{T}_n^+$. We show that a rectangle has a signed tiling by $\\mathcal{T}_n$ if and only if both sides of the rectangle are even and one of them is divisible by $n$, or if one of the sides is odd and the other side is divisible by $n\\left (\\frac{n}{2}-2\\right ).$ We also show that a rectangle has a signed tiling by $\\mathcal{T}_n^+, n\\ge 6$ even, if and only"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00572","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"}