{"paper":{"title":"All $SL_2$-tilings come from infinite triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christine Bessenrodt, Peter Jorgensen, Thorsten Holm","submitted_at":"2016-03-30T09:57:16Z","abstract_excerpt":"An $SL_2$-tiling is a bi-infinite matrix of positive integers such that each adjacent 2 by 2 submatrix has determinant 1. Such tilings are infinite analogues of Conway-Coxeter friezes, and they have strong links to cluster algebras, combinatorics, mathematical physics, and representation theory.\n  We show that, by means of so-called Conway-Coxeter counting, every $SL_2$-tiling arises from a triangulation of the disc with two, three or four accumulation points.\n  This improves earlier results which only discovered $SL_2$-tilings with infinitely many entries equal to 1. Indeed, our methods show "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09103","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"}