{"paper":{"title":"A note on norms of signed sums of vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.MG","authors_text":"Giorgos Chasapis, Nikos Skarmogiannis","submitted_at":"2019-06-09T21:37:21Z","abstract_excerpt":"Our starting point is an improved version of a result of D. Hajela related to a question of Koml\\'{o}s: we show that if $f(n)$ is a function such that $\\lim\\limits_{n\\to\\infty }f(n)=\\infty $ and $f(n)=o(n)$, there exists $n_0=n_0(f)$ such that for every $n\\geqslant n_0$ and any $S\\subseteq \\{-1,1\\}^n$ with cardinality $|S|\\leqslant 2^{n/f(n)}$ one can find orthonormal vectors $x_1,\\ldots ,x_n\\in {\\mathbb R}^n$ that satisfy $$\\|\\epsilon_1x_1+\\cdots +\\epsilon_nx_n\\|_{\\infty }\\geqslant c\\sqrt{\\log f(n)}$$ for all $(\\epsilon_1,\\ldots ,\\epsilon_n)\\in S$. We obtain analogous results in the case wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03716","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"}