{"paper":{"title":"Discrete Brunn-Minkowski Inequality for subsets of the cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dmitry Krachun, J\\'ose Madrid, Lars Becker, Paata Ivanisvili","submitted_at":"2024-04-06T03:40:13Z","abstract_excerpt":"We show that for all $A, B \\subseteq \\{0,1,2\\}^{d}$ we have $$ |A+B|\\geq (|A||B|)^{\\log(5)/(2\\log(3))}. $$ We also show that for all finite $A,B \\subset \\mathbb{Z}^{d}$, and any $V \\subseteq\\{0,1\\}^{d}$ the inequality $$ |A+B+V|\\geq |A|^{1/p}|B|^{1/q}|V|^{\\log_{2}(p^{1/p}q^{1/q})} $$ holds for all $p \\in (1, \\infty)$, where $q=\\frac{p}{p-1}$ is the conjugate exponent of $p$. All the estimates are dimension free with the best possible exponents. We discuss applications to various related problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.04486","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.04486/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}