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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 \\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.02249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-08T04:14:50Z","cross_cats_sorted":[],"title_canon_sha256":"1d53c10d35e4ae6e5acde4cf10680f2c01b794334ef6b816471057bc985cef06","abstract_canon_sha256":"b5c36baf9d5562b8d5e552285e473993c371535dbc34957082c0ad44bfa57793"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:41.405244Z","signature_b64":"6cccj3fbaf01jutirUYa66azpkKY229C56EN9n1vtGHqKmRxveNUYI5csoPQL+M3x52lY+QaBP6Ihfg5ZBZsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78d815ac9084741e69c16a71488b0ca0d0cb48da2f721ebdecccb84e73f2638a","last_reissued_at":"2026-05-18T01:33:41.404478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:41.404478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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