{"paper":{"title":"Schreier graphs of the Basilica group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Alfredo Donno, Daniele D'Angeli, Michel Matter, Tatiana Nagnibeda","submitted_at":"2009-11-15T21:43:43Z","abstract_excerpt":"With any self-similar action of a finitely generated group $G$ of automorphisms of a regular rooted tree $T$ can be naturally associated an infinite sequence of finite graphs $\\{\\Gamma_n\\}_{n\\geq 1}$, where $\\Gamma_n$ is the Schreier graph of the action of $G$ on the $n$-th level of $T$. Moreover, the action of $G$ on $\\partial T$ gives rise to orbital Schreier graphs $\\Gamma_{\\xi}$, $\\xi\\in \\partial T$. Denoting by $\\xi_n$ the prefix of length $n$ of the infinite ray $\\xi$, the rooted graph $(\\Gamma_{\\xi},\\xi)$ is then the limit of the sequence of finite rooted graphs $\\{(\\Gamma_n,\\xi_n)\\}_{n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2915","kind":"arxiv","version":5},"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"}