{"paper":{"title":"A Note on the Expected Length of the Longest Common Subsequences of two i.i.d. Random Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chen Xu, Christian Houdr\\'e","submitted_at":"2017-03-22T14:52:51Z","abstract_excerpt":"We address a question and a conjecture on the expected length of the longest common subsequences of two i.i.d.$\\ $random permutations of $[n]:=\\{1,2,...,n\\}$. The question is resolved by showing that the minimal expectation is not attained in the uniform case. The conjecture asserts that $\\sqrt{n}$ is a lower bound on this expectation, but we only obtain $\\sqrt[3]{n}$ for it."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07691","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"}