{"paper":{"title":"Tackling the Minimal Superpermutation Problem","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Robin Houston","submitted_at":"2014-08-21T18:52:00Z","abstract_excerpt":"A superpermutation on $n$ symbols is a string that contains each of the $n!$ permutations of the $n$ symbols as a contiguous substring. The shortest superpermutation on $n$ symbols was conjectured to have length $\\sum_{i=1}^n i!$. The conjecture had been verified for $n \\leq 5$. We disprove it by exhibiting an explicit counterexample for $n=6$. This counterexample was found by encoding the problem as an instance of the (asymmetric) Traveling Salesman Problem, and searching for a solution using a powerful heuristic solver."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5108","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"}