{"paper":{"title":"Random induced subgraphs of Cayley graphs induced by transpositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Christian M. Reidys, Emma Y. Jin","submitted_at":"2009-09-22T16:40:00Z","abstract_excerpt":"In this paper we study random induced subgraphs of Cayley graphs of the symmetric group induced by an arbitrary minimal generating set of transpositions. A random induced subgraph of this Cayley graph is obtained by selecting permutations with independent probability, $\\lambda_n$. Our main result is that for any minimal generating set of transpositions, for probabilities $\\lambda_n=\\frac{1+\\epsilon_n}{n-1}$ where $n^{-{1/3}+\\delta}\\le \\epsilon_n<1$ and $\\delta>0$, a random induced subgraph has a.s. a unique largest component of size $\\wp(\\epsilon_n)\\frac{1+\\epsilon_n}{n-1}n!$, where $\\wp(\\epsi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4037","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"}