{"paper":{"title":"A Note on Value Sets of Polynomials over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alev Topuzo\\u{g}lu, Leyla I\\c{s}{\\i}k","submitted_at":"2017-01-22T11:44:43Z","abstract_excerpt":"Most results on the value sets $V_f$ of polynomials $f \\in \\mathbb{F}_q[x]$ relate the cardinality $|V_f|$ to the degree of $f$. In particular, the structure of the spectrum of the class of polynomials of a fixed degree $d$ is rather well known.\n  We consider a class $\\mathcal{F}_{q,n}$ of polynomials, which we obtain by modifying linear permutations at $n$ points. The study of the spectrum of $\\mathcal{F}_{q,n}$ enables us to obtain a simple description of polynomials $F \\in \\mathcal{F}_{q,n}$ with prescribed $V_F$, especially those avoiding a given set, like cosets of subgroups of the multip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06158","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"}