{"paper":{"title":"Induced bisecting families for hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Niranjan Balachandran, Rogers Mathew, Sudebkumar Prasant Pal, Tapas Kumar Mishra","submitted_at":"2016-10-01T14:21:06Z","abstract_excerpt":"Two $n$-dimensional vectors $A$ and $B$, $A,B \\in \\mathbb{R}^n$, are said to be \\emph{trivially orthogonal} if in every coordinate $i \\in [n]$, at least one of $A(i)$ or $B(i)$ is zero. Given the $n$-dimensional Hamming cube $\\{0,1\\}^n$, we study the minimum cardinality of a set $\\mathcal{V}$ of $n$-dimensional $\\{-1,0,1\\}$ vectors, each containing exactly $d$ non-zero entries, such that every `possible' point $A \\in \\{0,1\\}^n$ in the Hamming cube has some $V \\in \\mathcal{V}$ which is orthogonal, but not trivially orthogonal, to $A$. We give asymptotically tight lower and (constructive) upper "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00140","kind":"arxiv","version":3},"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"}