{"paper":{"title":"Growth of Schreier graphs of automaton groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Ievgen Bondarenko","submitted_at":"2011-01-17T13:09:21Z","abstract_excerpt":"Every automaton group naturally acts on the space $X^\\omega$ of infinite sequences over some alphabet $X$. For every $w\\in X^\\omega$ we consider the Schreier graph $\\Gamma_w$ of the action of the group on the orbit of $w$. We prove that for a large class of automaton groups all Schreier graphs $\\Gamma_w$ have subexponential growth bounded above by $n^{(\\log n)^m}$ with some constant $m$. In particular, this holds for all groups generated by automata with polynomial activity growth (in terms of S.Sidki), confirming a conjecture of V.Nekrashevych. We present applications to omega-periodic graphs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3200","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"}