{"paper":{"title":"Partition-Symmetrical Entropy Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Qi Chen, Raymond W. Yeung","submitted_at":"2014-07-28T13:16:08Z","abstract_excerpt":"Let $\\cal{N}=\\{1,\\cdots,n\\}$. The entropy function $\\bf h$ of a set of $n$ discrete random variables $\\{X_i:i\\in\\cal N\\}$ is a $2^n$-dimensional vector whose entries are ${\\bf{h}}({\\cal{A}})\\triangleq H(X_{\\cal{A}}),\\cal{A}\\subset{\\cal N} $, the (joint) entropies of the subsets of the set of $n$ random variables with $H(X_\\emptyset)=0$ by convention. The set of all entropy functions for $n$ discrete random variables, denoted by $\\Gamma^*_n$, is called the entropy function region for $n$. Characterization of $\\Gamma^*_n$ and its closure $\\overline{\\Gamma^*_n}$ are well-known open problems in in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7405","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":""},"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"}