{"paper":{"title":"Alon's Nullstellensatz for multisets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"G\\'eza K\\'os, Lajos R\\'onyai","submitted_at":"2010-08-17T14:06:49Z","abstract_excerpt":"Alon's combinatorial Nullstellensatz (Theorem 1.1 from \\cite{Alon1}) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let $\\F$ be a field, $S_1,S_2,..., S_n$ be finite nonempty subsets of $\\F$. Alon's theorem is a specialized, precise version of the Hilbertsche Nullstellensatz for the ideal of all polynomial functions vanishing on the set $S=S_1\\times S_2\\times ... \\times S_n\\subseteq \\F^n$. From this Alon deduces a simple and amazingly widely applicable nonvanishing criterion (Theorem 1.2 in \\cite{Alon1}). It provides a sufficient condition f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2901","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":""},"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"}