{"paper":{"title":"Polyhedral and Tropical Geometry of Flag Positroids","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Christopher Eur, Jonathan Boretsky, Lauren Williams","submitted_at":"2022-08-19T03:05:09Z","abstract_excerpt":"A flag positroid of ranks $\\boldsymbol{r}:=(r_1<\\dots <r_k)$ on $[n]$ is a flag matroid that can be realized by a real $r_k \\times n$ matrix $A$ such that the $r_i \\times r_i$ minors of $A$ involving rows $1,2,\\dots,r_i$ are nonnegative for all $1\\leq i \\leq k$. In this paper we explore the polyhedral and tropical geometry of flag positroids, particularly when $\\boldsymbol{r}:=(a, a+1,\\dots,b)$ is a sequence of consecutive numbers. In this case we show that the nonnegative tropical flag variety TrFl$_{\\boldsymbol{r},n}^{\\geq 0}$ equals the nonnegative flag Dressian FlDr$_{\\boldsymbol{r},n}^{\\g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.09131","kind":"arxiv","version":5},"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/2208.09131/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"}