{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:N5NGN62WZGLXHLBFYPOGOAG2RH","short_pith_number":"pith:N5NGN62W","schema_version":"1.0","canonical_sha256":"6f5a66fb56c99773ac25c3dc6700da89d6ddfa5c097903d1b29f14062a7c20df","source":{"kind":"arxiv","id":"1510.02021","version":3},"attestation_state":"computed","paper":{"title":"Large classes of permutation polynomials over $\\mathbb{F}_{q^2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dingyi Pei, Pingzhi Yuan, Yanbin Zheng","submitted_at":"2015-10-07T16:39:16Z","abstract_excerpt":"Permutation polynomials (PPs) of the form $(x^{q} -x + c)^{\\frac{q^2 -1}{3}+1} +x$ over $\\mathbb{F}_{q^2}$ were presented by Li, Helleseth and Tang [Finite Fields Appl. 22 (2013) 16--23]. More recently, we have constructed PPs of the form $(x^{q} +bx + c)^{\\frac{q^2 -1}{d}+1} -bx$ over $\\mathbb{F}_{q^2}$, where $d=2, 3, 4, 6$ [Finite Fields Appl. 35 (2015) 215--230]. In this paper we concentrate our efforts on the PPs of more general form\n  \\[\n  f(x)=(ax^{q} +bx +c)^r \\phi((ax^{q} +bx +c)^{(q^2 -1)/d}) +ux^{q} +vx~~\\text{over $\\mathbb{F}_{q^2}$},\n  \\]\n  where $a,b,c,u,v \\in \\mathbb{F}_{q^2}$, "},"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":"1510.02021","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-07T16:39:16Z","cross_cats_sorted":[],"title_canon_sha256":"376f70bb7d53c6665569107b53ce472524b488a022924bb075c9dcfbd088184e","abstract_canon_sha256":"62d8593f94aa0aa57a13bd15f12ffd4b1d8bf88b47913d5b3350efbb0b142275"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:59.981582Z","signature_b64":"Y+7K4XmjN0j6nD0tf65+cPAhJLyorWFpjIy9SYJ5mJEk9i/Q393dVHiz6bkFStp49ppdKf0jbwmP/vhHs37ADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f5a66fb56c99773ac25c3dc6700da89d6ddfa5c097903d1b29f14062a7c20df","last_reissued_at":"2026-05-17T23:57:59.981169Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:59.981169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large classes of permutation polynomials over $\\mathbb{F}_{q^2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dingyi Pei, Pingzhi Yuan, Yanbin Zheng","submitted_at":"2015-10-07T16:39:16Z","abstract_excerpt":"Permutation polynomials (PPs) of the form $(x^{q} -x + c)^{\\frac{q^2 -1}{3}+1} +x$ over $\\mathbb{F}_{q^2}$ were presented by Li, Helleseth and Tang [Finite Fields Appl. 22 (2013) 16--23]. More recently, we have constructed PPs of the form $(x^{q} +bx + c)^{\\frac{q^2 -1}{d}+1} -bx$ over $\\mathbb{F}_{q^2}$, where $d=2, 3, 4, 6$ [Finite Fields Appl. 35 (2015) 215--230]. In this paper we concentrate our efforts on the PPs of more general form\n  \\[\n  f(x)=(ax^{q} +bx +c)^r \\phi((ax^{q} +bx +c)^{(q^2 -1)/d}) +ux^{q} +vx~~\\text{over $\\mathbb{F}_{q^2}$},\n  \\]\n  where $a,b,c,u,v \\in \\mathbb{F}_{q^2}$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02021","kind":"arxiv","version":3},"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":"1510.02021","created_at":"2026-05-17T23:57:59.981228+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.02021v3","created_at":"2026-05-17T23:57:59.981228+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02021","created_at":"2026-05-17T23:57:59.981228+00:00"},{"alias_kind":"pith_short_12","alias_value":"N5NGN62WZGLX","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"N5NGN62WZGLXHLBF","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"N5NGN62W","created_at":"2026-05-18T12:29:32.376354+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/N5NGN62WZGLXHLBFYPOGOAG2RH","json":"https://pith.science/pith/N5NGN62WZGLXHLBFYPOGOAG2RH.json","graph_json":"https://pith.science/api/pith-number/N5NGN62WZGLXHLBFYPOGOAG2RH/graph.json","events_json":"https://pith.science/api/pith-number/N5NGN62WZGLXHLBFYPOGOAG2RH/events.json","paper":"https://pith.science/paper/N5NGN62W"},"agent_actions":{"view_html":"https://pith.science/pith/N5NGN62WZGLXHLBFYPOGOAG2RH","download_json":"https://pith.science/pith/N5NGN62WZGLXHLBFYPOGOAG2RH.json","view_paper":"https://pith.science/paper/N5NGN62W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.02021&json=true","fetch_graph":"https://pith.science/api/pith-number/N5NGN62WZGLXHLBFYPOGOAG2RH/graph.json","fetch_events":"https://pith.science/api/pith-number/N5NGN62WZGLXHLBFYPOGOAG2RH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N5NGN62WZGLXHLBFYPOGOAG2RH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N5NGN62WZGLXHLBFYPOGOAG2RH/action/storage_attestation","attest_author":"https://pith.science/pith/N5NGN62WZGLXHLBFYPOGOAG2RH/action/author_attestation","sign_citation":"https://pith.science/pith/N5NGN62WZGLXHLBFYPOGOAG2RH/action/citation_signature","submit_replication":"https://pith.science/pith/N5NGN62WZGLXHLBFYPOGOAG2RH/action/replication_record"}},"created_at":"2026-05-17T23:57:59.981228+00:00","updated_at":"2026-05-17T23:57:59.981228+00:00"}