{"paper":{"title":"The parity search problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian Reiher","submitted_at":"2016-03-20T00:00:46Z","abstract_excerpt":"We prove that for any positive integers $n$ and $d$ there exists a collection consisting of $f=d\\log n+O(1)$ subsets $A_1, A_2, \\ldots, A_f$ of $[n]$ such that for any two distinct subsets $X$ and $Y$ of $[n]$ whose size is at most $d$ there is an index $i\\in [f]$ for which $| A_i\\cap X|$ and $|A_i\\cap Y|$ have different parity. Here we think of $d$ as fixed whereas $n$ is thought of as tending to infinity, and the base of the logarithm is $2$.\n  Translated into the language of combinatorial search theory, this tells us that \\[\n  d \\log n+O(1) \\] queries suffice to identify up to $d$ marked it"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06164","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"}