{"paper":{"title":"Weighted blade arrangements and the positive tropical Grassmannian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.CO","authors_text":"Nick Early","submitted_at":"2020-05-25T18:00:20Z","abstract_excerpt":"In this paper, we continue our study of blade arrangements and the positroidal subdivisions which are induced by them on $\\Delta_{k,n}$. A blade is a tropical hypersurface which is generated by a system of $n$ affine simple roots of type $SL_n$ that enjoys a cyclic symmetry. When placed at the center of a simplex, a blade induces a decomposition into $n$ maximal cells which are known as Pitman-Stanley polytopes.\n  We introduce a complex $(B_{k,n},\\partial)$ of weighted blade arrangements and we prove that the positive tropical Grassmannian surjects onto the top component of the complex, such t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.12305","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2005.12305/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"}