{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:IQYC4KSVU66VRWUVGQJ2XUWYNQ","short_pith_number":"pith:IQYC4KSV","schema_version":"1.0","canonical_sha256":"44302e2a55a7bd58da953413abd2d86c3f7d54a227402bc1a904bf57d56815ed","source":{"kind":"arxiv","id":"1807.01062","version":1},"attestation_state":"computed","paper":{"title":"Positivity of iterated sequences of polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bao-Xuan Zhu","submitted_at":"2018-07-03T10:03:29Z","abstract_excerpt":"In this paper, we present some criteria for the $2$-$q$-log-convexity and $3$-$q$-log-convexity of combinatorial sequences, which can be regarded as the first column of certain infinite triangular array $[A_{n,k}(q)]_{n,k\\geq0}$ of polynomials in $q$ with nonnegative coefficients satisfying the recurrence relation $$A_{n,k}(q)=A_{n-1,k-1}(q)+g_k(q)A_{n-1,k}(q)+h_{k+1}(q)A_{n-1,k+1}(q).$$ Those criterions can also be presented by continued fractions and generating functions. These allow a unified treatment of the $2$-$q$-log-convexity of alternating Eulerian polynomials, $2$-log-convexity of Eu"},"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":"1807.01062","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-03T10:03:29Z","cross_cats_sorted":[],"title_canon_sha256":"d61336e3bbecef675939179c84371f4ef52d1d9f8c95a032c3c121b52c742718","abstract_canon_sha256":"61ef7134ad0a0a85e744fc274eea425366e2353d3df5aa95f3b6cdc18262cd0c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:45.507373Z","signature_b64":"3bvzEZzGta/mUW3dIg92H1nhF/cYvM/WJS7pGYFnBchYJc6kWGoVHjuwfya0O2D+apCOTlaNM6RtuyAbyEwWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44302e2a55a7bd58da953413abd2d86c3f7d54a227402bc1a904bf57d56815ed","last_reissued_at":"2026-05-18T00:11:45.506712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:45.506712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positivity of iterated sequences of polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bao-Xuan Zhu","submitted_at":"2018-07-03T10:03:29Z","abstract_excerpt":"In this paper, we present some criteria for the $2$-$q$-log-convexity and $3$-$q$-log-convexity of combinatorial sequences, which can be regarded as the first column of certain infinite triangular array $[A_{n,k}(q)]_{n,k\\geq0}$ of polynomials in $q$ with nonnegative coefficients satisfying the recurrence relation $$A_{n,k}(q)=A_{n-1,k-1}(q)+g_k(q)A_{n-1,k}(q)+h_{k+1}(q)A_{n-1,k+1}(q).$$ Those criterions can also be presented by continued fractions and generating functions. These allow a unified treatment of the $2$-$q$-log-convexity of alternating Eulerian polynomials, $2$-log-convexity of Eu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01062","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.01062","created_at":"2026-05-18T00:11:45.506805+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.01062v1","created_at":"2026-05-18T00:11:45.506805+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01062","created_at":"2026-05-18T00:11:45.506805+00:00"},{"alias_kind":"pith_short_12","alias_value":"IQYC4KSVU66V","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"IQYC4KSVU66VRWUV","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"IQYC4KSV","created_at":"2026-05-18T12:32:31.084164+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IQYC4KSVU66VRWUVGQJ2XUWYNQ","json":"https://pith.science/pith/IQYC4KSVU66VRWUVGQJ2XUWYNQ.json","graph_json":"https://pith.science/api/pith-number/IQYC4KSVU66VRWUVGQJ2XUWYNQ/graph.json","events_json":"https://pith.science/api/pith-number/IQYC4KSVU66VRWUVGQJ2XUWYNQ/events.json","paper":"https://pith.science/paper/IQYC4KSV"},"agent_actions":{"view_html":"https://pith.science/pith/IQYC4KSVU66VRWUVGQJ2XUWYNQ","download_json":"https://pith.science/pith/IQYC4KSVU66VRWUVGQJ2XUWYNQ.json","view_paper":"https://pith.science/paper/IQYC4KSV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.01062&json=true","fetch_graph":"https://pith.science/api/pith-number/IQYC4KSVU66VRWUVGQJ2XUWYNQ/graph.json","fetch_events":"https://pith.science/api/pith-number/IQYC4KSVU66VRWUVGQJ2XUWYNQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IQYC4KSVU66VRWUVGQJ2XUWYNQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IQYC4KSVU66VRWUVGQJ2XUWYNQ/action/storage_attestation","attest_author":"https://pith.science/pith/IQYC4KSVU66VRWUVGQJ2XUWYNQ/action/author_attestation","sign_citation":"https://pith.science/pith/IQYC4KSVU66VRWUVGQJ2XUWYNQ/action/citation_signature","submit_replication":"https://pith.science/pith/IQYC4KSVU66VRWUVGQJ2XUWYNQ/action/replication_record"}},"created_at":"2026-05-18T00:11:45.506805+00:00","updated_at":"2026-05-18T00:11:45.506805+00:00"}