{"paper":{"title":"Bases in which some numbers have exactly two expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Derong Kong, Vilmos Komornik","submitted_at":"2017-05-01T11:17:05Z","abstract_excerpt":"In this paper we answer several questions raised by Sidorov on the set $\\mathcal B_2$ of bases in which there exist numbers with exactly two expansions. In particular, we prove that the set $\\mathcal B_2$ is closed, and it contains both infinitely many isolated and accumulation points in $(1, q_{KL})$, where $q_{KL}\\approx 1.78723$ is the Komornik-Loreti constant. Consequently we show that the second smallest element of $\\mathcal B_2$ is the smallest accumulation point of $\\mathcal B_2$. We also investigate the higher order derived sets of $\\mathcal B_2$. Finally, we prove that there exists a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00473","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"}