{"paper":{"title":"How Uniform is the Uniform Distribution on Permutations?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michael D. Perlman","submitted_at":"2019-01-10T20:55:48Z","abstract_excerpt":"For large $q$, does the (discrete) uniform distribution on the set of $q!$ permutations of the vector $(1,2,\\dots,q)$ closely approximate the (continuous) uniform distribution on the $(q-2)$-sphere that contains them? These permutations comprise the vertices of the regular permutohedron, a $(q-1)$-dimensional convex polyhedron. Surprisingly to me, the answer is emphatically no: these permutations are confined to a negligible portion of the sphere, and the regular permutohedron occupies a negligible portion of the ball. However, $(1,2,\\dots,q)$ is not the most favorable configuration for approx"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03386","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"}