{"paper":{"title":"Linear combinations of Rademacher random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Harrie Hendriks, Martien C.A. van Zuijlen","submitted_at":"2017-03-21T14:53:56Z","abstract_excerpt":"For a fixed unit vector $a=(a_1,a_2,\\ldots,a_n)\\in S^{n-1}$, we consider the $2^n$ sign vectors $\\varepsilon=(\\varepsilon^1,\\varepsilon^2,\\ldots,\\varepsilon^n)\\in \\{+1,-1\\}^n$ and the corresponding scalar products $\\varepsilon\\cdot a=\\sum_{i=1}^n \\varepsilon^ia_i$. In this paper we will solve for $n=1,2,\\ldots,9$ an old conjecture stating that of the $2^n$ sums of the form $\\sum\\pm a_i$ it is impossible that there are more with $|\\sum_{i=1}^n \\pm a_i|>1$ than there are with $|\\sum_{i=1}^n \\pm a_i|\\leq1$. Although the problem has been solved completely in case the $a_i$'s are equal, the more ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07251","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"}