{"paper":{"title":"Some intriguing upper bounds for separating hash families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Chong Shangguan, Gennian Ge, Xin Wang","submitted_at":"2017-07-06T12:54:36Z","abstract_excerpt":"An $N\\times n$ matrix on $q$ symbols is called $\\{w_1,\\ldots,w_t\\}$-separating if for arbitrary $t$ pairwise disjoint column sets $C_1,\\ldots,C_t$ with $|C_i|=w_i$ for $1\\le i\\le t$, there exists a row $f$ such that $f(C_1),\\ldots,f(C_t)$ are also pairwise disjoint, where $f(C_i)$ denotes the collection of components of $C_i$ restricted to row $f$.\n  Given integers $N,q$ and $w_1,\\ldots,w_t$, denote by $C(N,q,\\{w_1,\\ldots,w_t\\})$ the maximal $n$ such that a corresponding matrix does exist.\n  The determination of $C(N,q,\\{w_1,\\ldots,w_t\\})$ has received remarkable attentions during the recent y"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01758","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"}