{"paper":{"title":"Random generation under the Ewens distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.GR","authors_text":"Sean Eberhard","submitted_at":"2018-08-27T15:46:17Z","abstract_excerpt":"The Ewens sampling formula with parameter $\\alpha$ is the distribution on $S_n$ which gives each $\\pi\\in S_n$ weight proportional to $\\alpha^{C(\\pi)}$, where $C(\\pi)$ is the number of cycles of $\\pi$. We show that, for any fixed $\\alpha$, two Ewens-random permutations generate at least $A_n$ with high probability. More generally we work out how many permutations are needed for $\\alpha$ growing with $n$. Roughly speaking, two are needed for $0 \\leq \\alpha \\ll n^{1/2}$, three for $n^{1/2} \\ll \\alpha \\ll n^{2/3}$, etc."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08892","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"}