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For each $n\\geq 1$ the set of integers $k$ such that there exist $\\mu$ latin squares of order $n$ with $k$ intersection is denoted by $I^{\\mu}[n]$. In a paper by P. Adams et al. (2002), $I^3[n]$ is determined completely. In this paper we completely determine $I^4[n]$ for $n\\geq 16$. For $n \\le 16$, we find out most of the elements of $I^4[n]$."},"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":"1408.6725","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-27T05:18:09Z","cross_cats_sorted":[],"title_canon_sha256":"27eec9a24979cdc47dc177a2dad40ae070a921cd84771c577a56fb97572af48c","abstract_canon_sha256":"a3a5aec0c2753387432b802ec6e8712aaa1299ac58bd6672d2aeeec2bde033c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:57.799934Z","signature_b64":"Lg/waRhKGfOrgCVrZvy0HVu3XfmjESNVMFsJNOXLdYGnE/gc5IUWQ8/+QQNYFT6KqS+sSXnaxRL4DkgSb/0XBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c81d2e6de18071ae7253996da47254735ef530d9b39510feaefd41d24872d225","last_reissued_at":"2026-05-18T01:32:57.799309Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:57.799309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The four-way intersection problem for latin squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"E. 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