{"paper":{"title":"A complete characterization of a family of permutation trinomials over $\\mathbb F_{p^2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marco Timpanella","submitted_at":"2026-06-07T19:59:52Z","abstract_excerpt":"Let $p>3$ be a prime and let $$f_{\\lambda_1,\\lambda_2}(x)=x^{p^2-p+1}+\\lambda_1x^{p^2}+\\lambda_2x^{2p-1}\\in\\mathbb F_{p^2}[x].$$ We determine all pairs $(\\lambda_1,\\lambda_2)\\in(\\mathbb F_{p^2})^2$ for which $f_{\\lambda_1,\\lambda_2}$ is a permutation polynomial of $\\mathbb F_{p^2}$. The final classification consists of three explicit families. The first one is the binomial case $\\lambda_1=0$. The other two are obtained from the condition $\\lambda_2=c\\lambda_1^3$, with $c\\in \\mathbb F_{p}^{*}$, and are defined by two simple equations involving the norm $\\lambda_1^{p+1}$. The proof is based on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08809","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08809/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}