{"paper":{"title":"A Cauchy-Davenport theorem for linear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"John Kim, Simao Herdade, Swastik Kopparty","submitted_at":"2015-08-10T00:36:57Z","abstract_excerpt":"We prove a version of the Cauchy-Davenport theorem for general linear maps. For subsets $A,B$ of the finite field $\\mathbb{F}_p$, the classical Cauchy-Davenport theorem gives a lower bound for the size of the sumset $A+B$ in terms of the sizes of the sets $A$ and $B$. Our theorem considers a general linear map $L: \\mathbb{F}_p^n \\to \\mathbb{F}_p^m$, and subsets $A_1, \\ldots, A_n \\subseteq \\mathbb{F}_p$, and gives a lower bound on the size of $L(A_1 \\times A_2 \\times \\ldots \\times A_n)$ in terms of the sizes of the sets $A_1, \\ldots, A_n$.\n  Our proof uses Alon's Combinatorial Nullstellensatz a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02100","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"}