{"paper":{"title":"Intercalates and Discrepancy in Random Latin Squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Matthew Kwan","submitted_at":"2016-07-18T08:58:43Z","abstract_excerpt":"An intercalate in a Latin square is a $2\\times2$ Latin subsquare. Let $N$ be the number of intercalates in a uniformly random $n\\times n$ Latin square. We prove that asymptotically almost surely $N\\ge\\left(1-o\\left(1\\right)\\right)\\,n^{2}/4$, and that $\\mathbb{E}N\\le\\left(1+o\\left(1\\right)\\right)\\,n^{2}/2$ (therefore asymptotically almost surely $N\\le fn^{2}$ for any $f\\to\\infty$). This significantly improves the previous best lower and upper bounds. We also give an upper tail bound for the number of intercalates in two fixed rows of a random Latin square. In addition, we discuss a problem of L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04981","kind":"arxiv","version":2},"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"}