{"paper":{"title":"Envelope Word and Gap Sequence in Doubling Sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hanxiong Zhang, Yuke Huang","submitted_at":"2014-08-23T13:30:29Z","abstract_excerpt":"Let $\\omega$ be a factor of Doubling sequence $D_\\infty=x_1x_2\\cdots$, then it occurs in the sequence infinitely many times. Let $\\omega_p$ be the $p$-th occurrence of $\\omega$ and $G_p(\\omega)$ be the gap between $\\omega_p$ and $\\omega_{p+1}$. In this paper, we discuss the structure of the gap sequence $\\{G_p(\\omega)\\}_{p\\geq1}$. We prove that all factors can be divided into two types, one type has exactly two distinct gaps $G_1(\\omega)$ and $G_2(\\omega)$, the other type has exactly three distinct gaps $G_1(\\omega)$, $G_2(\\omega)$ and $G_4(\\omega)$. We determine the expressions of gaps comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5495","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"}