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On the face stratification of the $m=2$ amplituhedron

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arxiv 2403.06948 v3 pith:BSP7KSTR submitted 2024-03-11 math.CO hep-thmath-phmath.AGmath.MP

Thomas Lam This is my paper · ORCID
classification math.COhep-thmath-phmath.AGmath.MP
keywords faceamplituhedronlukowskiposetstratificationconfirmconsistentconstruction
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We define and study the face stratification of the m=2 amplituhedron. We show that the face poset is an upper order ideal in the face poset of the totally nonnegative Grassmannian. Our construction is consistent with earlier work of Lukowski, and we confirm various predictions of Lukowski.

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  1. Exterior Cyclic Polytopes and Convexity of Amplituhedra

    math.CO 2025-07 conditional novelty 7.0 of 10

    For k=m=2, the amplituhedron equals the intersection of Gr(2,4) with the exterior cyclic polytope C_{2,2,n}(Z), and its extendable convex dual is the twisted amplituhedron.

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