{"paper":{"title":"Completions of epsilon-dense partial Latin squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Padraic Bartlett","submitted_at":"2012-05-07T23:10:00Z","abstract_excerpt":"A classical question in combinatorics is the following: given a partial latin square P, when can we complete P to a latin square L? In this paper, we will investigate the class of \\leq\\epsilon-dense partial latin squares: partial latin squares in which each symbol, row, and column contains \\leq\\epsilon n-many nonblank cells. A conjecture of Nash-Williams on triangulations of graphs led Daykin and H\\\"aggkvist to conjecture that all \\leq(1/4)-dense partial latin squares are completable. In this paper, we will discuss the proof methods and results used in previous attempts to resolve this conject"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1558","kind":"arxiv","version":4},"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"}