{"paper":{"title":"Incidence geometry and universality in the tropical plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Catherine Lee, Dhruv Ranganathan, Michelle Jones, Milo Brandt","submitted_at":"2017-09-01T15:34:32Z","abstract_excerpt":"We examine the incidence geometry of lines in the tropical plane. We prove tropical analogs of the Sylvester-Gallai and Motzkin-Rabin theorems in classical incidence geometry. This study leads naturally to a discussion of the realizability of incidence data of tropical lines. Drawing inspiration from the von Staudt constructions and Mn\\\"ev's universality theorem, we prove that determining whether a given tropical linear incidence datum is realizable by a tropical line arrangement requires solving an arbitrary linear programming problem over the integers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00366","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":""},"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"}