{"paper":{"title":"Towards extending the Ahlswede-Khachatrian theorem to cross t-intersecting families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark Siggers, Norihide Tokushige, Sang June Lee","submitted_at":"2015-09-08T04:14:50Z","abstract_excerpt":"Ahlswede and Khachatrian's diametric theorem is a weighted version of their complete intersection theorem, itself an extension of the $t$-intersecting Erd\\H{o}s-Ko-Rado theorem. Their intersection theorem says that the maximum size of a family of subsets of $[n] = \\{1, \\dots, n\\}$, every pair of which intersects in at least $t$ elements, is the size of certain trivially intersecting families proposed by Frankl. We address a cross intersecting version of their diametric theorem.\n  Two families $\\mathcal{A}$ and $\\mathcal{B}$ of subsets of $[n]$ are {\\em cross $t$-intersecting} if for every $A \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02249","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"}