{"paper":{"title":"On a family of Schreier graphs of intermediate growth associated with a self-similar group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Alfredo Donno, Ievgen Bondarenko, Tullio Ceccherini-Silberstein, Volodymyr Nekrashevych","submitted_at":"2011-06-20T18:16:12Z","abstract_excerpt":"For every infinite sequence $\\omega=x_1,x_2,...$, with $x_i\\in\\{0,1\\}$, we construct an infinite 4-regular graph $X_{\\omega}$. These graphs are precisely the Schreier graphs of the action of a certain self-similar group on the space $\\{0,1\\}^{\\infty}$. We solve the isomorphism and local isomorphism problems for these graphs, and determine their automorphism groups. Finally, we prove that all graphs $X_\\omega$ have intermediate growth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3979","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"}