{"paper":{"title":"On the Boundaries of the m=2 Amplituhedron","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"hep-th","authors_text":"Tomasz Lukowski","submitted_at":"2019-08-01T13:30:16Z","abstract_excerpt":"Amplituhedra $\\mathcal{A}_{n,k}^{(m)}$ are geometric objects of great interest in modern mathematics and physics: for mathematicians they are combinatorially rich generalizations of polygons and polytopes, based on the notion of positivity; for physicists, the amplituhedron $\\mathcal{A}^{(4)}_{n,k}$ encodes the scattering amplitudes of the planar $\\mathcal{N}=4$ super Yang-Mills theory. In this paper we study the structure of boundaries for the amplituhedron $\\mathcal{A}_{n,k}^{(2)}$. We classify all boundaries of all dimensions and provide their graphical enumeration. We find that the boundar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00386","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/1908.00386/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"}