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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 $\\tau=4132$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1410.0230","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-01T14:10:31Z","cross_cats_sorted":[],"title_canon_sha256":"49313ea6f7dfd18a0914dff8985a04ad1b5f91617754763857b97e190101b180","abstract_canon_sha256":"37fb8b454df802ce1331bbab0461e8334720f9863e557bc9f13fbb3d3d6c387a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:14.771914Z","signature_b64":"//OeGqdhk45KO710nfOOz/UAOB2KZi1sE8Be1gWn8yT0tPjB7ci5W+9wAKmGi4+aZgVoZKlyLbufxVsJ9bGnDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b9b8b91fbc17fbcce6c4d7dd0be457c0d875714636d117e9310de3546b0e60f","last_reissued_at":"2026-05-18T01:28:14.771109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:14.771109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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