{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4YEB6QFBMAIJGSUJ2LGMQ2S2F5","short_pith_number":"pith:4YEB6QFB","schema_version":"1.0","canonical_sha256":"e6081f40a16010934a89d2ccc86a5a2f7051655c1754e188b0e552ca1ac09b9f","source":{"kind":"arxiv","id":"1407.1968","version":2},"attestation_state":"computed","paper":{"title":"Strong q-log-convexity of the Eulerian polynomials of Coxeter groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bao-Xuan Zhu, Lily Li Liu","submitted_at":"2014-07-08T06:31:45Z","abstract_excerpt":"In this paper we prove the strong $q$-log-convexity of the Eulerian polynomials of Coxeter groups using their exponential generating functions. Our proof is based on the theory of exponential Riordan arraya and a criterion for determining the strong $q$-log-convexity of polynomials sequences, whose generating functions can be given by the continued fraction. As consequences, we get the strong $q$-log-convexity the Eulerian polynomials of type $A_n,B_n$, their $q$-analogous and the generalized Eulerian polynomials associated to the arithmetic progression $\\{a,a+d,a+2d,a+3d,\\ldots\\}$ in a unifie"},"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":"1407.1968","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-08T06:31:45Z","cross_cats_sorted":[],"title_canon_sha256":"460c11011c60eb44c43c0818937813bb763cf85d0354c2ecfa0a5ff93241106a","abstract_canon_sha256":"2d4314c101dc10caa03949021a53a7879d8c344c927308add82e1081f26ec0a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:46.765608Z","signature_b64":"OpG4xg5na6TRRf7SsVV+IN5a2328eFnL0fwLLj3navArYx5LCn42iqmUabJ04/nXyGM6LmymP6IYC1CxDxs3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6081f40a16010934a89d2ccc86a5a2f7051655c1754e188b0e552ca1ac09b9f","last_reissued_at":"2026-05-18T02:43:46.765165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:46.765165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong q-log-convexity of the Eulerian polynomials of Coxeter groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bao-Xuan Zhu, Lily Li Liu","submitted_at":"2014-07-08T06:31:45Z","abstract_excerpt":"In this paper we prove the strong $q$-log-convexity of the Eulerian polynomials of Coxeter groups using their exponential generating functions. Our proof is based on the theory of exponential Riordan arraya and a criterion for determining the strong $q$-log-convexity of polynomials sequences, whose generating functions can be given by the continued fraction. As consequences, we get the strong $q$-log-convexity the Eulerian polynomials of type $A_n,B_n$, their $q$-analogous and the generalized Eulerian polynomials associated to the arithmetic progression $\\{a,a+d,a+2d,a+3d,\\ldots\\}$ in a unifie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1968","kind":"arxiv","version":2},"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":"1407.1968","created_at":"2026-05-18T02:43:46.765225+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.1968v2","created_at":"2026-05-18T02:43:46.765225+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1968","created_at":"2026-05-18T02:43:46.765225+00:00"},{"alias_kind":"pith_short_12","alias_value":"4YEB6QFBMAIJ","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4YEB6QFBMAIJGSUJ","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4YEB6QFB","created_at":"2026-05-18T12:28:14.216126+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/4YEB6QFBMAIJGSUJ2LGMQ2S2F5","json":"https://pith.science/pith/4YEB6QFBMAIJGSUJ2LGMQ2S2F5.json","graph_json":"https://pith.science/api/pith-number/4YEB6QFBMAIJGSUJ2LGMQ2S2F5/graph.json","events_json":"https://pith.science/api/pith-number/4YEB6QFBMAIJGSUJ2LGMQ2S2F5/events.json","paper":"https://pith.science/paper/4YEB6QFB"},"agent_actions":{"view_html":"https://pith.science/pith/4YEB6QFBMAIJGSUJ2LGMQ2S2F5","download_json":"https://pith.science/pith/4YEB6QFBMAIJGSUJ2LGMQ2S2F5.json","view_paper":"https://pith.science/paper/4YEB6QFB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.1968&json=true","fetch_graph":"https://pith.science/api/pith-number/4YEB6QFBMAIJGSUJ2LGMQ2S2F5/graph.json","fetch_events":"https://pith.science/api/pith-number/4YEB6QFBMAIJGSUJ2LGMQ2S2F5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4YEB6QFBMAIJGSUJ2LGMQ2S2F5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4YEB6QFBMAIJGSUJ2LGMQ2S2F5/action/storage_attestation","attest_author":"https://pith.science/pith/4YEB6QFBMAIJGSUJ2LGMQ2S2F5/action/author_attestation","sign_citation":"https://pith.science/pith/4YEB6QFBMAIJGSUJ2LGMQ2S2F5/action/citation_signature","submit_replication":"https://pith.science/pith/4YEB6QFBMAIJGSUJ2LGMQ2S2F5/action/replication_record"}},"created_at":"2026-05-18T02:43:46.765225+00:00","updated_at":"2026-05-18T02:43:46.765225+00:00"}