{"paper":{"title":"The m=2 amplituhedron and the hypersimplex: signs, clusters, triangulations, Eulerian numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.AG","math.MP"],"primary_cat":"math.CO","authors_text":"Lauren Williams, Matteo Parisi, Melissa Sherman-Bennett","submitted_at":"2021-04-16T17:37:05Z","abstract_excerpt":"The hypersimplex $\\Delta_{k+1,n}$ is the image of the positive Grassmannian $Gr^{\\geq 0}_{k+1,n}$ under the moment map. It is a polytope of dimension $n-1$ in $\\mathbb{R}^n$. Meanwhile, the amplituhedron $\\mathcal{A}_{n,k,2}(Z)$ is the projection of the positive Grassmannian $Gr^{\\geq 0}_{k,n}$ into $Gr_{k,k+2}$ under a map $\\tilde{Z}$ induced by a matrix $Z\\in \\text{Mat}_{n,k+2}^{>0}$. Introduced in the context of scattering amplitudes, it is not a polytope, and has dimension $2k$. Nevertheless, there seem to be remarkable connections between these two objects via T-duality, as was first note"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.08254","kind":"arxiv","version":4},"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/2104.08254/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"}