On the (5,3)-Grassmannian and the p-Frame Potentials

Daniel Riley, Kasso Okoudjou

Session: General

Keywords: p-frame potentials, frame force, tight frames, Grassmannian frames, coherence, equiangular tight frames, optimization

TL;DR: We show that the (5,3)-Grassmannian frame does not minimize any p-frame potential, and that no configuration is a minimizer with N=5 in d=3 for all sufficiently large p.

Abstract: This paper establishes that the minimizing configuration for the p-frame potentials with 5 points in 3 dimensions is not the (5,3)-Grassmannian frame for any finite p, and shows that no configuration can minimize the p-frame potentials for N=5 in d=3 for all sufficiently large p. To prove this, a family of 5-point configurations parameterized by the value of p is explicitly constructed, and it is shown to be a smooth interpolation between the known solution at p=2 and the (5,3)-Grassmannian frame, evolving under a set of coupled differential equations.

Submission Number: 105