{"paper":{"title":"Numbers with integer expansion in the numeration system with negative base","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"D. Dombek, E. Pelantov\\'a, P. Ambro\\v{z}, Z. Mas\\'akova","submitted_at":"2009-12-23T10:27:13Z","abstract_excerpt":"In this paper, we study representations of real numbers in the positional numeration system with negative basis, as introduced by Ito and Sadahiro. We focus on the set $\\Z_{-\\beta}$ of numbers whose representation uses only non-negative powers of $-\\beta$, the so-called $(-\\beta)$-integers. We describe the distances between consecutive elements of $\\Z_{-\\beta}$. In case that this set is non-trivial we associate to $\\beta$ an infinite word $\\boldsymbol{v}_{-\\beta}$ over an (in general infinite) alphabet. The self-similarity of $\\Z_{-\\beta}$, i.e., the property $-\\beta \\Z_{-\\beta}\\subset \\Z_{-\\b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4597","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"}