{"paper":{"title":"On Lipschitz Bijections between Boolean Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"cs.DM","authors_text":"Igor Shinkar, Shravas Rao","submitted_at":"2015-01-13T14:28:29Z","abstract_excerpt":"For two functions $f,g:\\{0,1\\}^n\\to\\{0,1\\}$ a mapping $\\psi:\\{0,1\\}^n\\to\\{0,1\\}^n$ is said to be a $\\textit{mapping from $f$ to $g$}$ if it is a bijection and $f(z)=g(\\psi(z))$ for every $z\\in\\{0,1\\}^n$. In this paper we study Lipschitz mappings between boolean functions.\n  Our first result gives a construction of a $C$-Lipschitz mapping from the ${\\sf Majority}$ function to the ${\\sf Dictator}$ function for some universal constant $C$. On the other hand, there is no $n/2$-Lipschitz mapping in the other direction, namely from the ${\\sf Dictator}$ function to the ${\\sf Majority}$ function. This"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03016","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"}