{"paper":{"title":"Four Random Permutations Conjugated by an Adversary Generate $S_n$ with High Probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Igor Rivin, Robin Pemantle, Yuval Peres","submitted_at":"2014-12-11T19:59:25Z","abstract_excerpt":"We prove a conjecture dating back to a 1978 paper of D.R.\\ Musser~\\cite{musserirred}, namely that four random permutations in the symmetric group $\\mathcal{S}_n$ generate a transitive subgroup with probability $p_n > \\epsilon$ for some $\\epsilon > 0$ independent of $n$, even when an adversary is allowed to conjugate each of the four by a possibly different element of $\\S_n$ (in other words, the cycle types already guarantee generation of $\\mathcal{S}_n$). This is closely related to the following random set model. A random set $M \\subseteq \\mathbb{Z}^+$ is generated by including each $n \\geq 1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3781","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"}