{"paper":{"title":"Application of Character Estimates to the Number of $T_2$-Systems of the Alternating Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Stefan-Christoph Virchow","submitted_at":"2017-10-27T10:40:48Z","abstract_excerpt":"We use character theory and character estimates to show that the number of $T_2$-systems of $A_n$ is at least \\begin{equation*} \\frac{1}{8n\\sqrt{3}}\\exp\\left(\\frac{2\\pi}{\\sqrt{6}}n^{1/2}\\right)(1+o(1)). \\end{equation*} Applying this result, we obtain a lower bound for the number of connected components of the product replacement graph $\\Gamma_2(A_n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10063","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"}