{"paper":{"title":"Intersection theorems for $\\{0,\\pm 1\\}$-vectors and $s$-cross-intersecting families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andrey Kupavskii, Peter Frankl","submitted_at":"2016-03-03T00:20:22Z","abstract_excerpt":"In this paper we study two directions of extending the classical Erd\\H os-Ko-Rado theorem which states that any family of $k$-element subsets of the set $[n] = \\{1,\\ldots,n\\}$ in which any two sets intersect, has cardinality at most ${n-1\\choose k-1}$.\n  In the first part of the paper we study the families of $\\{0,\\pm 1\\}$-vectors. Denote by $\\mathcal L_k$ the family of all vectors $\\mathbf v$ from $\\{0,\\pm 1\\}^n$ such that $\\langle\\mathbf v,\\mathbf v\\rangle = k$. For any $k$, most $l$ and sufficiently large $n$ we determine the maximal size of the family $\\mathcal V\\subset \\mathcal L_k$ such "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00938","kind":"arxiv","version":4},"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"}