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

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.

12 pages. v2: minor changes. v3: minor changes