{"paper":{"title":"On the Entropy of a Two Step Random Fibonacci Substitution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CO","authors_text":"Johan Nilsson","submitted_at":"2013-03-11T14:06:53Z","abstract_excerpt":"We consider a random generalisation of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping $\\mathtt{a}\\mapsto \\mathtt{baa}$ and $\\mathtt{b} \\mapsto \\mathtt{ab}$ with probability $p$ and $\\mathtt{b} \\mapsto \\mathtt{ba}$ with probability $1-p$ for $0<p<1$ and where the random rule is applied each time it acts on a $\\mathtt{b}$. We show that the topological entropy of this object is given by the growth rate of the set of inflated random Fibonacci words, and we exactly calculate its value."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2526","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"}