{"paper":{"title":"Variations on Narrow Dots-and-Boxes and Dots-and-Triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"math.CO","authors_text":"Adam Jobson, D. Jacob Wildstrom, Levi Sledd, Susan C. White","submitted_at":"2015-07-30T23:45:43Z","abstract_excerpt":"We verify a conjecture of Nowakowski and Ottaway that closed $1 \\times n$ Dots-and-Triangles is a first-player win when $n \\neq 2$. We also prove that in both the open and closed $1 \\times n$ Dots-and-Boxes games where $n$ is even, the first player can guarantee a tie."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08707","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"}