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Many mathematicians have paid much attention to congruences on some special colored partition functions. In this paper, we investigate the general colored partition functions. Given positive integers $1=s_1<s_2<\\dots <s_k$ and $\\ell_1, \\ell_2,\\dots , \\ell_k$. Let $g(\\mathbf{s}, \\mathbf{l}, n)$ be the number of $\\ell$-colored pa"},"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":"1610.05938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-19T09:44:45Z","cross_cats_sorted":[],"title_canon_sha256":"63cd8d508e2370d8475ae7eaf6d4d410ac48e36260f7cb0e3d6bcd20b01bb8ac","abstract_canon_sha256":"9eb5087b318c4fec44aedb0a19d3a67632ecd9b81de97df3f4ef2d95c7649a75"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:50.634424Z","signature_b64":"/9hS17VHPPyWnVFXAJ2sasaI4Z1mZuWHGnxx78t8SnhFBavBcQsGTYIwUr3WaPUQqWW5LrQcrYL4LH6Y9D0jAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"562564afd47e75553ae160e036385e5d0b25312eaa87b8fbefad64a596ca4136","last_reissued_at":"2026-05-18T01:01:50.633687Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:50.633687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic formulas for general colored partition functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ya-Li Li, Yong-Gao Chen","submitted_at":"2016-10-19T09:44:45Z","abstract_excerpt":"In 1917, Hardy and Ramanujan obtained the asymptotic formula for the classical partition function $p(n)$. 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