{"paper":{"title":"Multigeometric sequences and Cantorvals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Artur Bartoszewicz, Emilia Szymonik, Ma{\\l}gorzata Filipczak","submitted_at":"2013-04-11T06:30:09Z","abstract_excerpt":"For a sequence $x \\in l_1 \\setminus c_{00}$, one can consider the achievement set $E(x)$ of all subsums of series $\\sum_{n=1}^{\\infty} x(n)$. It is known that $E(x)$ is one of the following types of sets:\n  * finite union of closed intervals,\n  * homeomorphic to the Cantor set,\n  * homeomorphic to the set $T$ of subsums of $\\sum_{n=1}^{\\infty} c(n)$ where $c(2n-1)=\\frac{3}{4^n}$ and $c(2n)=\\frac{2}{4^n}$ (Cantorval).\n  Based on ideas of Jones and Velleman, and Guthrie and Nymann we describe families of sequences which contain, according to our knowledge, all known examples of $x$'s with $E(x)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4218","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"}