Combinatorics of the geometry of Wilson loop diagrams II: Grassmann necklaces, dimensions, and denominators

Abstract Wilson loop diagrams are an important tool in studying scattering amplitudes of SYM $N=4$ theory and known by previous work to be associated positroids. In this paper, we study the structure positroids, as well denominator integrand defined each diagram. We give algorithm derive Grassmann necklace positroid directly from diagram, a recursive proof that dimension these cells is thrice number propagators also show ideal generated radical product minors.