{"paper":{"title":"On the Geometry of the Birkhoff Polytope. II. The Schatten $p$-norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Fr\\'ed\\'eric Morneau-Gu\\'erin, Javad Mashreghi, Ludovick Bouthat","submitted_at":"2023-10-21T15:40:32Z","abstract_excerpt":"In the first of this series of two articles, we studied some geometrical aspects of the Birkhoff polytope, the compact convex set of all $n \\times n$ doubly stochastic matrices, namely the Chebyshev center, and the Chebyshev radius of the Birkhoff polytope associated with metrics induced by the operator norms from $\\ell_n^p$ to $\\ell_n^p$ for $1 \\leq p \\leq \\infty$. In the present paper, we take another look at those very questions, but for a different family of matrix norms, namely the Schatten $p$-norms, for $1 \\leq p < \\infty$. While studying these properties, the intrinsic connection to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.14043","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.14043/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"}