{"paper":{"title":"Stanley-Wilf limits are typically exponential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jacob Fox","submitted_at":"2013-10-31T04:25:37Z","abstract_excerpt":"For a permutation $\\pi$, let $S_{n}(\\pi)$ be the number of permutations on $n$ letters avoiding $\\pi$. Marcus and Tardos proved the celebrated Stanley-Wilf conjecture that $L(\\pi)= \\lim_{n \\to \\infty} S_n(\\pi)^{1/n}$ exists and is finite. Backed by numerical evidence, it has been conjectured by many researchers over the years that $L(\\pi)=\\Theta(k^2)$ for every permutation $\\pi$ on $k$ letters. We disprove this conjecture, showing that $L(\\pi)=2^{k^{\\Theta(1)}}$ for almost all permutations $\\pi$ on $k$ letters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8378","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"}