{"paper":{"title":"Egge triples and unbalanced Wilf-equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Burstein, Jonathan Bloom","submitted_at":"2014-10-01T14:10:31Z","abstract_excerpt":"Egge conjectured that permutations avoiding the set of patterns $\\{2143,3142,\\tau\\}$, where $\\tau\\in\\{246135,254613,263514,524361,546132\\}$, are enumerated by the large Schr\\\"oder numbers. Consequently, $\\{2143,3142,\\tau\\}$ with $\\tau$ as above is Wilf-equivalent to the set of patterns $\\{2413,3142\\}$. Burstein and Pantone proved the case of $\\tau=246135$. We prove the remaining four cases. As a byproduct of our proof, we also enumerate the case $\\tau=4132$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0230","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"}