{"paper":{"title":"Fence Complexes and Toric Degenerations of Positroid Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Cameron Chang, Josephine Hlavinka, Pranav Enugandla","submitted_at":"2026-06-11T02:19:45Z","abstract_excerpt":"We associate to each positroid variety in the Grassmannian $\\mathrm{Gr}(k,n)$ a polyhedral complex, which we call a fence complex. Fence complexes consist of unions of faces of the Gelfand-Tsetlin polytope $P_{k,n}$ associated to a fundamental weight $\\omega_k$. We show that these fence complexes are homeomorphic to closed balls. Furthermore, they endow the Gelfand-Tsetlin polytope with the structure of a regular CW complex, giving a polyhedral complex presentation of the regular CW complex structure on $\\mathrm{Gr}(k,n)_{\\geq 0}$. We also show that the Ehrhart polynomial of a fence complex eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12815","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/2606.12815/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"}