{"paper":{"title":"A decomposition theorem for balanced measures","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ansel Goh, Gregory Baimetov, Owen Jacobs, Raymond Guo, Ryan Bushling, Sean Lee","submitted_at":"2023-12-14T04:14:15Z","abstract_excerpt":"Let $G = (V,E)$ be a connected graph. A probability measure $\\mu$ on $V$ is called \"balanced\" if it has the following property: if $T_\\mu(v)$ denotes the \"earth mover's\" cost of transporting all the mass of $\\mu$ from all over the graph to the vertex $v$, then $T_\\mu$ attains its global maximum at each point in the support of $\\mu$. We prove a decomposition result that characterizes balanced measures as convex combinations of suitable \"extremal\" balanced measures that we call \"basic.\" An upper bound on the number of basic balanced measures on $G$ follows, and an example shows that this estimat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.08649","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.08649/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"}