{"paper":{"title":"Comparing weighted difference and earth mover's distance via Young diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"William Q. Erickson","submitted_at":"2021-04-15T06:58:04Z","abstract_excerpt":"We consider two natural statistics on pairs of histograms, in which the $n$ bins have weights $0, \\ldots, n-1$. The difference ($\\mathbf{D}$) between the weighted totals of the histograms is, in a sense, refined by the earth mover's distance ($\\mathbf{EMD}$), which measures the amount of work required to equalize the histograms. We were recently surprised, however, by how little $\\mathbf{EMD}$ actually does refine $\\mathbf{D}$ in certain real-world applications, which led to the main problem in this paper: what is the probability that $\\mathbf{EMD} = |\\mathbf{D}|$? We derive a formula for this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.07273","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/2104.07273/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"}