On the face stratification of the $m=2$ amplituhedron
Thomas Lam
TL;DR
This paper investigates the face stratification of the m=2 amplituhedron, revealing its relation to the face poset of the totally nonnegative Grassmannian and confirming previous predictions.
Contribution
It introduces a new understanding of the face stratification of the m=2 amplituhedron and its connection to the nonnegative Grassmannian, aligning with prior theoretical predictions.
Findings
Face poset is an upper order ideal in the nonnegative Grassmannian
Construction aligns with earlier work of Lukowski
Confirmed various predictions of Lukowski
Abstract
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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Taxonomy
TopicsMathematics and Applications · Computational Geometry and Mesh Generation · Point processes and geometric inequalities