{"paper":{"title":"Structure of transition classes for factor codes on shifts of finite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mahsa Allahbakhshi, Soonjo Hong, Uijin Jung","submitted_at":"2013-11-22T20:46:39Z","abstract_excerpt":"Given a factor code $\\pi$ from a shift of finite type $X$ onto a sofic shift $Y$, the class degree of $\\pi$ is defined to be the minimal number of transition classes over points of $Y$. In this paper we investigate structure of transition classes and present several dynamical properties analogous to the properties of fibers of finite-to-one codes. As a corollary, we show that for an irreducible factor triple there cannot be a transition between two different transition classes over a right transitive point, answering a question raised by Quas."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5878","kind":"arxiv","version":3},"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"}