{"paper":{"title":"On univoque and strongly univoque sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pieter C. Allaart","submitted_at":"2016-01-18T20:17:35Z","abstract_excerpt":"Much has been written about expansions of real numbers in noninteger bases. Particularly, for a finite alphabet $\\{0,1,\\dots,\\alpha\\}$ and a real number (base) $1<\\beta<\\alpha+1$, the so-called {\\em univoque set} of numbers which have a unique expansion in base $\\beta$ has garnered a great deal of attention in recent years. Motivated by recent applications of $\\beta$-expansions to Bernoulli convolutions and a certain class of self-affine functions, we introduce the notion of a {\\em strongly univoque} set. We study in detail the set $D_\\beta$ of numbers which are univoque but not strongly univo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04680","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"}