{"paper":{"title":"Functional Graphs of Polynomials over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.NT","authors_text":"Bernard Mans, Florian Luca, Igor E. Shparlinski, Luke Mathieson, Min Sha, Sergei V. Konyagin","submitted_at":"2013-07-10T09:01:24Z","abstract_excerpt":"Given a function $f$ in a finite field ${\\mathbb F}_q$ of $q$ elements, we define the functional graph of $f$ as a directed graph on $q$ nodes labelled by the elements of ${\\mathbb F}_q$ where there is an edge from $u$ to $v$ if and only if $f(u) = v$. We obtain some theoretic estimates on the number of non-isomorphic graphs generated by all polynomials of a given degree. We then develop a simple and practical algorithm to test the isomorphism of quadratic polynomials that has linear memory and time complexities. Furthermore, we extend this isomorphism testing algorithm to the general case of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2718","kind":"arxiv","version":3},"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"}