{"paper":{"title":"Permutation polynomials of finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Christopher J. Shallue","submitted_at":"2012-11-23T01:25:49Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be the finite field of $q$ elements. Then a \\emph{permutation polynomial} (PP) of $\\mathbb{F}_q$ is a polynomial $f \\in \\mathbb{F}_q[x]$ such that the associated function $c \\mapsto f(c)$ is a permutation of the elements of $\\mathbb{F}_q$. In 1897 Dickson gave what he claimed to be a complete list of PPs of degree at most 6, however there have been suggestions recently that this classification might be incomplete. Unfortunately, Dickson's claim of a full characterisation is not easily verified because his published proof is difficult to follow. This is mainly due to antiquat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6044","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"}