{"paper":{"title":"Zero-sum subsequences in bounded-sum $\\{-1, 1\\}$-sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Adriana Hansberg, Amanda Montejano, Yair Caro","submitted_at":"2016-12-20T06:35:53Z","abstract_excerpt":"The following result gives the flavor of this paper: Let $t$, $k$ and $q$ be integers such that $q\\geq 0$, $0\\leq t < k$ and $t \\equiv k \\,({\\rm mod}\\, 2)$, and let $s\\in [0,t+1]$ be the unique integer satisfying $s \\equiv q + \\frac{k-t-2}{2} \\,({\\rm mod} \\, (t+2))$. Then for any integer $n$ such that \\[n \\ge \\max\\left\\{k,\\frac{1}{2(t+2)}k^2 + \\frac{q-s}{t+2}k - \\frac{t}{2} + s\\right\\}\\] and any function $f:[n]\\to \\{-1,1\\}$ with $|\\sum_{i=1}^nf(i)| \\le q$, there is a set $B \\subseteq [n]$ of $k$ consecutive integers with $|\\sum_{y\\in B}f(y)| \\le t$. Moreover, this bound is sharp for all the pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06523","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"}