No abstract

Two decades ago, Zauner conjectured that for every dimension d, there exists an equiangular tight frame consisting of d 2 vectors in C d . Most progress to date explicitly constructs the promised frame in various dimensions, and it now appears that a constructive proof of Zauner's conjecture may require progress on the Stark conjectures. In this paper, we propose an alternative approach involving biangular Gabor frames that may eventually lead to an unconditional non-constructive proof of Zauner's conjecture.

The line packing problem is concerned with the optimal packing of points in real or complex projective space so that the minimum distance between points is maximized. Until recently, all bounds on optimal line packings were known to be derivable from Delsarte's linear program. Last year, Bukh and Cox introduced a new bound for the line packing problem using completely different techniques. In this paper, we use ideas from the Bukh-Cox proof to find a new proof of the Welch bound, and then we use ideas from Delsarte's linear program to find a new proof of the Bukh-Cox bound. Hopefully, these unifying principles will lead to further refinements.

No abstract

We apply the method of moments to prove a recent conjecture of Haikin, Zamir and Gavish [16] concerning the distribution of the singular values of random subensembles of Paley equiangular tight frames. Our analysis applies more generally to real equiangular tight frames of redundancy 2, and we suspect similar ideas will eventually produce more general results for arbitrary choices of redundancy.