{"paper":{"title":"Minimum number of additive tuples in groups of prime order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Katherine Staden, Oleg Pikhurko, Ostap Chervak","submitted_at":"2017-10-05T09:25:33Z","abstract_excerpt":"For a prime number $p$ and a sequence of integers $a_0,\\dots,a_k\\in \\{0,1,\\dots,p\\}$, let $s(a_0,\\dots,a_k)$ be the minimum number of $(k+1)$-tuples $(x_0,\\dots,x_k)\\in A_0\\times\\dots\\times A_k$ with $x_0=x_1+\\dots + x_k$, over subsets $A_0,\\dots,A_k\\subseteq\\mathbb{Z}_p$ of sizes $a_0,\\dots,a_k$ respectively. An elegant argument of Lev (independently rediscovered by Samotij and Sudakov) shows that there exists an extremal configuration with all sets $A_i$ being intervals of appropriate length, and that the same conclusion also holds for the related problem, reposed by Bajnok, when $a_0=\\dots="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01936","kind":"arxiv","version":4},"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"}