{"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. S. Mahmoodian, H. Minooei, M. Mohammadi Nevisi, P. Adams","submitted_at":"2014-08-27T05:18:09Z","abstract_excerpt":"For $\\mu$ given latin squares of order $n$, they have {\\sf $k$ intersection} when they have $k$ identical cells and $n^2-k$ cells with mutually different entries. 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 $I^4[n]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6725","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"}