{"paper":{"title":"Improved Lower Bounds for Permutation Arrays Using Permutation Rational Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Brian Malouf, I. Hal Sudborough, Linda Morales, Sergey Bereg, Thomas Stanley","submitted_at":"2020-03-23T04:07:07Z","abstract_excerpt":"We consider rational functions of the form $V(x)/U(x)$, where both $V(x)$ and $U(x)$ are polynomials over the finite field $\\mathbb{F}_q$. Polynomials that permute the elements of a field, called {\\it permutation polynomials ($PPs$)}, have been the subject of research for decades. Let ${\\mathcal P}^1(\\mathbb{F}_q)$ denote $\\mathbb{Z}_q \\cup \\{\\infty\\}$. If the rational function, $V(x)/U(x)$, permutes the elements of ${\\mathcal P}^1(\\mathbb{F}_q)$, it is called a {\\em permutation rational function (PRf)}. Let $N_d(q)$ denote the number of PPs of degree $d$ over $\\mathbb{F}_q$, and let $N_{v,u}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.10072","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.10072/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"}