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By imitating a result of Liu and Wang on generating new $q$-log-convex sequences of polynomials from old ones, we obtain a sufficient condition for determining the $q$-log-convexity of self-reciprocal polynomials. Based on this criterion, we then give an affirmative answer to Sun's conjecture."},"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":"1308.2736","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-13T01:58:43Z","cross_cats_sorted":[],"title_canon_sha256":"73a65f69fb397d40bb8c87fa3dbbb2bee1450891c4329f179e40a60c5b086a8e","abstract_canon_sha256":"9071ef7d2fd087feaafa1d7f88ce0d396b34846d7411fae1346d6b1cf1b67620"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:55.387010Z","signature_b64":"NYbr3SytP8V0mpvpsLPmKJtdBwtwI3/S811sF9BL2tpYCxuYoShNo4XLXXZT3+Uq8OC1OjXnKjSGwrCGxFmnDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16f8d00dfff3447d9b0cbfb5f10cf1e234065497e969ffaae60d4705286e3f08","last_reissued_at":"2026-05-18T03:15:55.386340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:55.386340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the $q$-log-convexity conjecture of Sun","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anne X.Y. Ren, Donna Q.J. Dou","submitted_at":"2013-08-13T01:58:43Z","abstract_excerpt":"In his study of Ramanujan-Sato type series for $1/\\pi$, Sun introduced a sequence of polynomials $S_n(q)$ as given by $$S_n(q)=\\sum\\limits_{k=0}^n{n\\choose k}{2k\\choose k}{2(n-k)\\choose n-k}q^k,$$ and he conjectured that the polynomials $S_n(q)$ are $q$-log-convex. By imitating a result of Liu and Wang on generating new $q$-log-convex sequences of polynomials from old ones, we obtain a sufficient condition for determining the $q$-log-convexity of self-reciprocal polynomials. 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