{"paper":{"title":"Internal edge vectors on plabic networks in the disk and a generalization of Talaska formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"Petr G. Grinevich, Simonetta Abenda","submitted_at":"2021-08-06T17:59:32Z","abstract_excerpt":"Following [42], positroid cells ${\\mathcal S}_{\\mathcal M}^{\\mbox{TNN}}$ in totally non-negative Grassmannians ${Gr^{\\mbox{TNN}} (k,n)}$ admit parametrizations by positive weights on planar bicolored directed perfect networks in the disk. An explicit formula for elements of matrices representing the points in ${\\mathcal S}_{\\mathcal M}^{\\mbox{TNN}}$ was obtained in [49] in terms of flows on such networks. The formulas from [42,49] are defined on the boundary edge vectors. In this paper we propose an extension of these formulas for vectors on internal edges defined as summations over paths on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.03229","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/2108.03229/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"}