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These congruences have then been complemented and generalized to the case of $r$-Fishburn numbers by F. Garvan. In this note, we answer a question of Andrews and Sellers regarding an extension of these congruences to the case of prime powers. We show that, under a certain condition, all these congruences indee"},"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":"1407.7521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-28T19:59:09Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8f7ffafe337f9fac60103b084282e9534b030a3cbab34b31a42c6ae27ee584dc","abstract_canon_sha256":"187f1cb0531a4bb5d804e3730b08f0ad429b9f194f45228f7daad247e5de439e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:27.051098Z","signature_b64":"RnPdcdlznoos6sjcj6lE1ZNIhuJVzEtw5NIhdzD2JeXhL3xfPlEUqh7AHbqROffJ8YaA5fKs2bh2EFjKaSl4CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfe5ff6ec7791cae11af95249b7605700d06da72bf754c566d81010d20f0fff1","last_reissued_at":"2026-05-18T02:07:27.050701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:27.050701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Congruences for Fishburn numbers modulo prime powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Armin Straub","submitted_at":"2014-07-28T19:59:09Z","abstract_excerpt":"The Fishburn numbers $\\xi (n)$ are defined by the formal power series \\[ \\sum_{n \\geq 0} \\xi (n) q^n = \\sum_{n \\geq 0} \\prod_{j = 1}^n (1 - (1 - q)^j). \\] Recently, G. 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