{"paper":{"title":"Chv\\'{a}tal's Conjecture and Correlation Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ehud Friedgut, Gil Kalai, Jeff Kahn, Nathan Keller","submitted_at":"2016-08-31T17:21:57Z","abstract_excerpt":"Chv\\'{a}tal's conjecture in extremal combinatorics asserts that for any decreasing family $\\mathcal{F}$ of subsets of a finite set $S$, there is a largest intersecting subfamily of $\\mathcal{F}$ consisting of all members of $\\mathcal{F}$ that include a particular $x \\in S$. In this paper we reformulate the conjecture in terms of influences of variables on Boolean functions and correlation inequalities, and study special cases and variants using tools from discrete Fourier analysis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08954","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"}