{"paper":{"title":"Tiling groupoids and Bratteli diagrams II: structure of the orbit equivalence relation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.DS","authors_text":"Antoine Julien, Jean Savinien","submitted_at":"2010-05-17T16:18:35Z","abstract_excerpt":"In this second paper, we study the case of substitution tilings of R^d. The substitution on tiles induces substitutions on the faces of the tiles of all dimensions j=0, ..., d-1. We reconstruct the tiling's equivalence relation in a purely combinatorial way using the AF-relations given by the lower dimensional substitutions. We define a Bratteli multi-diagram B which is made of the Bratteli diagrams B^j, j=0, ..., d, of all those substitutions. The set of infinite paths in B^d is identified with the canonical transversal Xi of the tiling. Any such path has a \"border\", which is a set of tails i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2965","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"}