{"paper":{"title":"A New Approach to Permutation Polynomials over Finite Fields, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Neranga Fernando, Stephen D. Lappano, Xiang-dong Hou","submitted_at":"2012-08-14T18:58:08Z","abstract_excerpt":"Let $p$ be a prime and $q$ a power of $p$. For $n\\ge 0$, let $g_{n,q}\\in\\Bbb F_p[{\\tt x}]$ be the polynomial defined by the functional equation $\\sum_{a\\in\\Bbb F_q}({\\tt x}+a)^n=g_{n,q}({\\tt x}^q-{\\tt x})$. When is $g_{n,q}$ a permutation polynomial (PP) of $\\Bbb F_{q^e}$? This turns out to be a challenging question with remarkable breath and depth, as shown in the predecessor of the present paper. We call a triple of positive integers $(n,e;q)$ {\\em desirable} if $g_{n,q}$ is a PP of $\\Bbb F_{q^e}$. In the present paper, we find many new classes of desirable triples whose corresponding PPs we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2942","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"}