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These bounds follow from a more general result showing that a permutation avoiding a pattern of a special form is a merge of two permutations, each of which avoids a smaller pattern. If the conjecture is true that the maximum Stanley-Wilf limit for patterns of length $\\ell$ is attained by a layered pattern then this implies an upper bound of $4\\ell^2$ for the Stanley-Wilf limit of any pattern of length $\\ell$.\n  We als"},"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":"1111.5736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-24T12:08:13Z","cross_cats_sorted":[],"title_canon_sha256":"0f84023d261bee71dd3d36ad6c39d1eea9b65f262159bc272202f420c0de82f7","abstract_canon_sha256":"874a8c69875eed1aa3618644d187ef278a9b8c5d07d8992fa22767f41443adf7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:53.200662Z","signature_b64":"ENgyPAT0DAB+1xa3XWZAOwInbdoNyu2rJUDAW/CO9/GAs8ih06FtmhaOY4Rk3TJzQbQ7i+3dBK3E4eQGxpDaCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ada181c3992151e3169ebcfcad9d77189a12a26dabbb985e6fb8fa44ee8a0ae","last_reissued_at":"2026-05-18T03:52:53.200086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:53.200086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Upper bounds for the Stanley-Wilf limit of 1324 and other layered patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anders Claesson, Einar Steingr\\'imsson, V\\'it Jel\\'inek","submitted_at":"2011-11-24T12:08:13Z","abstract_excerpt":"We prove that the Stanley-Wilf limit of any layered permutation pattern of length $\\ell$ is at most $4\\ell^2$, and that the Stanley-Wilf limit of the pattern 1324 is at most 16. These bounds follow from a more general result showing that a permutation avoiding a pattern of a special form is a merge of two permutations, each of which avoids a smaller pattern. 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