{"paper":{"title":"Search Problems in Vector Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bal\\'azs Patk\\'os, Marcella Tak\\'ats, Tam\\'as H\\'eger","submitted_at":"2013-09-26T06:42:13Z","abstract_excerpt":"We consider the following $q$-analog of the basic combinatorial search problem: let $q$ be a prime power and $\\GF(q)$ the finite field of $q$ elements. Let $V$ denote an $n$-dimensional vector space over $\\GF(q)$ and let $\\mathbf{v}$ be an unknown 1-dimensional subspace of $V$. We will be interested in determining the minimum number of queries that is needed to find $\\mathbf{v}$ provided all queries are subspaces of $V$ and the answer to a query $U$ is YES if $\\mathbf{v} \\leqslant U$ and NO if $\\mathbf{v} \\not\\leqslant U$. This number will be denoted by $A(n,q)$ in the adaptive case (when for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6731","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"}