{"paper":{"title":"On the Sensitivity of k-Uniform Hypergraph Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Ang Li, Kevin Cuddy, Min Jae Song, Stella Biderman","submitted_at":"2015-10-01T18:19:55Z","abstract_excerpt":"In this paper we present a graph property with sensitivity $\\Theta(\\sqrt{n})$, where $n={v\\choose2}$ is the number of variables, and generalize it to a $k$-uniform hypergraph property with sensitivity $\\Theta(\\sqrt{n})$, where $n={v\\choose k}$ is again the number of variables. This yields the smallest sensitivity yet achieved for a $k$-uniform hypergraph property. We then show that, for even $k$, there is a $k$-uniform hypergraph property that demonstrates a quadratic gap between sensitivity and block sensitivity. This matches the largest known gap found by Ambainis and Sun (2011) for Boolean "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00354","kind":"arxiv","version":3},"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"}