{"paper":{"title":"Query complexity of sampling and small geometric partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"Luis Rademacher, Navin Goyal, Santosh Vempala","submitted_at":"2014-11-14T05:41:56Z","abstract_excerpt":"In this paper we study the following problem:\n  Discrete partitioning problem (DPP): Let $\\mathbb{F}_q P^n$ denote the $n$-dimensional finite projective space over $\\mathbb{F}_q$. For positive integer $k \\leq n$, let $\\{ A^i\\}_{i=1}^N$ be a partition of $(\\mathbb{F}_q P^n)^k$ such that\n  (1) for all $i \\leq N$, $A^i = \\prod_{j=1}^k A^i_j$ (partition into product sets),\n  (2) for all $i \\leq N$, there is a $(k-1)$-dimensional subspace $L^i \\subseteq \\mathbb{F}_q P^n$ such that $A^i \\subseteq (L^i)^k$.\n  What is the minimum value of $N$ as a function of $q,n,k$? We will be mainly interested in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3799","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"}