{"paper":{"title":"On the counting problem in inverse Littlewood--Offord theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Asaf Ferber, Kyle Luh, Vishesh Jain, Wojciech Samotij","submitted_at":"2019-04-23T17:05:13Z","abstract_excerpt":"Let $\\epsilon_1, \\dotsc, \\epsilon_n$ be i.i.d. Rademacher random variables taking values $\\pm 1$ with probability $1/2$ each. Given an integer vector $\\boldsymbol{a} = (a_1, \\dotsc, a_n)$, its concentration probability is the quantity $\\rho(\\boldsymbol{a}):=\\sup_{x\\in \\mathbb{Z}}\\Pr(\\epsilon_1 a_1+\\dots+\\epsilon_n a_n = x)$. The Littlewood-Offord problem asks for bounds on $\\rho(\\boldsymbol{a})$ under various hypotheses on $\\boldsymbol{a}$, whereas the inverse Littlewood-Offord problem, posed by Tao and Vu, asks for a characterization of all vectors $\\boldsymbol{a}$ for which $\\rho(\\boldsymbol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10425","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"}