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This extends a theorem of Coulter, Henderson and Matthews. Consequently, we generalize a result of Marcos by constructing permutation polynomials of the forms $x h(\\lambda_{j}(x))$ and $xh(\\mu_{j}(x))$, where $\\lambda_{j}(x)$ is the $j$-th elementary symmetric polynomial of $x, x^{q}, ..., x^{q^{m-1}}"},"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":"1303.2229","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-09T16:22:21Z","cross_cats_sorted":[],"title_canon_sha256":"7e9db7e2195f0015d5a2cdd9039b0df194ea2eead3849e6587058addcb4aea6f","abstract_canon_sha256":"8a5a39e38e8d65104558e4c0e522b5b2da1a34a09e0ecf10bc79bda685b41958"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:17.777925Z","signature_b64":"3leLBxrZNISDf/eq9OTM8vAPLeZkeFiXZkmsCk2YZQ0oLnimWN4A0a54U2had1WbGzwoBEq0YqRpZbHvJY+uBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"987fb171aff3e9729d236d63c7e982bcee6a4c074172460b244f3c0319acc491","last_reissued_at":"2026-05-17T23:53:17.777192Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:17.777192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructing permutation polynomials over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shaofang Hong, Xiaoer Qin","submitted_at":"2013-03-09T16:22:21Z","abstract_excerpt":"In this paper, we construct several new permutation polynomials over finite fields. 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Consequently, we generalize a result of Marcos by constructing permutation polynomials of the forms $x h(\\lambda_{j}(x))$ and $xh(\\mu_{j}(x))$, where $\\lambda_{j}(x)$ is the $j$-th elementary symmetric polynomial of $x, x^{q}, ..., x^{q^{m-1}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2229","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":"1303.2229","created_at":"2026-05-17T23:53:17.777307+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.2229v2","created_at":"2026-05-17T23:53:17.777307+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2229","created_at":"2026-05-17T23:53:17.777307+00:00"},{"alias_kind":"pith_short_12","alias_value":"TB73C4NP6PUX","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"TB73C4NP6PUXFHJD","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"TB73C4NP","created_at":"2026-05-18T12:27:59.945178+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/TB73C4NP6PUXFHJDNVR4P2MCXT","json":"https://pith.science/pith/TB73C4NP6PUXFHJDNVR4P2MCXT.json","graph_json":"https://pith.science/api/pith-number/TB73C4NP6PUXFHJDNVR4P2MCXT/graph.json","events_json":"https://pith.science/api/pith-number/TB73C4NP6PUXFHJDNVR4P2MCXT/events.json","paper":"https://pith.science/paper/TB73C4NP"},"agent_actions":{"view_html":"https://pith.science/pith/TB73C4NP6PUXFHJDNVR4P2MCXT","download_json":"https://pith.science/pith/TB73C4NP6PUXFHJDNVR4P2MCXT.json","view_paper":"https://pith.science/paper/TB73C4NP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.2229&json=true","fetch_graph":"https://pith.science/api/pith-number/TB73C4NP6PUXFHJDNVR4P2MCXT/graph.json","fetch_events":"https://pith.science/api/pith-number/TB73C4NP6PUXFHJDNVR4P2MCXT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TB73C4NP6PUXFHJDNVR4P2MCXT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TB73C4NP6PUXFHJDNVR4P2MCXT/action/storage_attestation","attest_author":"https://pith.science/pith/TB73C4NP6PUXFHJDNVR4P2MCXT/action/author_attestation","sign_citation":"https://pith.science/pith/TB73C4NP6PUXFHJDNVR4P2MCXT/action/citation_signature","submit_replication":"https://pith.science/pith/TB73C4NP6PUXFHJDNVR4P2MCXT/action/replication_record"}},"created_at":"2026-05-17T23:53:17.777307+00:00","updated_at":"2026-05-17T23:53:17.777307+00:00"}