{"paper":{"title":"Edge vectors on plabic networks in the disk and amalgamation of totally non-negative Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Petr G. Grinevich, Simonetta Abenda","submitted_at":"2019-08-20T15:41:22Z","abstract_excerpt":"Amalgamation in the totally non-negative part of positroid varieties is equivalent to gluing copies of $Gr^{TP}(1,3)$ and $Gr^{TP}(2,3)$. Lam has proposed to represent amalgamation in positroid varieties by equivalence classes of relations on bipartite graphs and identify total non-negativity via edge signatures. Here we provide an explicit characterization of such signatures on the planar bicolored trivalent directed perfect networks in the disk parametrizing positroid cells $S_M^{TNN}$.To a graph $G$ representing $S_M^{TNN}$, we associate a geometric signature satisfying full rank condition "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07437","kind":"arxiv","version":4},"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/1908.07437/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"}