{"paper":{"title":"SL_2-Tilings Do Not Exist in Higher Dimensions (mostly)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Dylan Rupel, Laurent Demonet, Pavel Tumarkin, Pierre-Guy Plamondon, Salvatore Stella","submitted_at":"2016-04-08T21:47:49Z","abstract_excerpt":"We define a family of generalizations of $\\operatorname{SL}_2$-tilings to higher dimensions called $\\boldsymbol{\\epsilon}$-$\\operatorname{SL}_2$-tilings. We show that, in each dimension 3 or greater, $\\boldsymbol{\\epsilon}$-$\\operatorname{SL}_2$-tilings exist only for certain choices of $\\boldsymbol{\\epsilon}$. In the case that they exist, we show that they are essentially unique and have a concrete description in terms of odd Fibonacci numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02491","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"}