{"paper":{"title":"Complete mappings and Carlitz rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alev Topuzo\\u{g}lu, Arne Winterhof, Leyla I\\c{s}{\\i}k","submitted_at":"2016-04-26T15:13:16Z","abstract_excerpt":"The well-known Chowla and Zassenhaus conjecture, proven by Cohen in 1990, states that for any $d\\ge 2$ and any prime $p>(d^2-3d+4)^2$ there is no complete mapping polynomial in $\\mathbb{F}_{p}[x]$ of degree $d$.\n  For arbitrary finite fields $\\mathbb{F}_{q}$, we give a similar result in terms of the Carlitz rank of a permutation polynomial rather than its degree. We prove that if $n<\\lfloor q/2\\rfloor$, then there is no complete mapping in $\\mathbb{F}_{q}[x]$ of Carlitz rank $n$ of small linearity. We also determine how far permutation polynomials $f$ of Carlitz rank $n<\\lfloor q/2\\rfloor$ are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07710","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"}