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We say that patterns $\\pi, \\tau \\in \\mathfrak{S}_m$ are strongly c-Wilf equivalent if for all $n$ and $k$, the number of permutations in $\\mathfrak{S}_n$ with exactly $k$ occurrences of $\\pi$ as a consecutive pattern is the same as for $\\tau$. In 2018, Dwyer and Elizalde conjectured (generalizing a conjecture of Elizalde from 2012) that if $\\pi,"},"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":"1807.04921","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-13T05:30:47Z","cross_cats_sorted":[],"title_canon_sha256":"1988badff5af6630a4eef9d7eb9113181e5bffd5a7993c62494a2175a6272ae8","abstract_canon_sha256":"95e3d375df0a9dd17f45c8b1fdd39428933466dadd98991f14075be2bf222ac2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:49.415304Z","signature_b64":"kAIv7VxzSsuroBb/M6yWt67JT6t7TfsPBQp1ElHumjzCbyktU0Z+SGqTsfKQGe3xpGR6CgG8WCjflWAVpy/CDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65e6351cbca294078e6bc79a9174d71e091f50a5c227e5dcb40ee9d6c663504a","last_reissued_at":"2026-05-18T00:10:49.414830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:49.414830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constraining Strong c-Wilf Equivalence Using Cluster Poset Asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ashwin Sah, Mitchell Lee","submitted_at":"2018-07-13T05:30:47Z","abstract_excerpt":"Let $\\pi \\in \\mathfrak{S}_m$ and $\\sigma \\in \\mathfrak{S}_n$ be permutations. An occurrence of $\\pi$ in $\\sigma$ as a consecutive pattern is a subsequence $\\sigma_i \\sigma_{i+1} \\cdots \\sigma_{i+m-1}$ of $\\sigma$ with the same order relations as $\\pi$. We say that patterns $\\pi, \\tau \\in \\mathfrak{S}_m$ are strongly c-Wilf equivalent if for all $n$ and $k$, the number of permutations in $\\mathfrak{S}_n$ with exactly $k$ occurrences of $\\pi$ as a consecutive pattern is the same as for $\\tau$. 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