{"paper":{"title":"Orbit length generating functions of automorphisms of a rooted regular binary tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Richard Pink","submitted_at":"2014-03-31T14:37:25Z","abstract_excerpt":"To every automorphism w of an infinite rooted regular binary tree we associate a two variable generating function \\Phi_w that encodes information on the orbit structure of w. We prove that this is a rational function if w can be described by finitely many recursion relations of a particular form. We show that this condition is satisfied for all elements of the discrete iterated monodromy group \\Gamma associated to a postcritically finite quadratic polynomial over C. For such \\Gamma we also prove that there are only finitely many possibilities for the denominator of \\Phi_w, and we describe a pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.8019","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"}