{"paper":{"title":"Transversals in Latin arrays with many distinct symbols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Darcy Best, David R. Wood, Ian M. Wanless, Kevin Hendrey, Tim E. Wilson","submitted_at":"2016-12-30T10:16:22Z","abstract_excerpt":"An array is row-Latin if no symbol is repeated within any row. An array is Latin if it and its transpose are both row-Latin. A transversal in an $n\\times n$ array is a selection of $n$ different symbols from different rows and different columns. We prove that every $n \\times n$ Latin array containing at least $(2-\\sqrt{2}) n^2$ distinct symbols has a transversal. Also, every $n \\times n$ row-Latin array containing at least $\\frac14(5-\\sqrt{5})n^2$ distinct symbols has a transversal. Finally, we show by computation that every Latin array of order $7$ has a transversal, and we describe all small"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09443","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"}