{"paper":{"title":"Conjugacy growth series for finitary wreath products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.NT","authors_text":"Madeline Locus","submitted_at":"2016-11-19T20:53:44Z","abstract_excerpt":"We examine the conjugacy growth series of all wreath products of the finitary permutation groups $\\text{Sym}(X)$ and $\\text{Alt}(X)$ for an infinite set $X$. We determine their asymptotics, and we characterize the limiting behavior between the $\\text{Alt}(X)$ and $\\text{Sym}(X)$ wreath products. In particular, their ratios form a limit if and only if the dimension of the symmetric wreath product is twice the dimension of the alternating wreath product."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06428","kind":"arxiv","version":3},"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"}