English

The Singer-Zauner gap for equiangular tight frames

Functional Analysis 2026-05-28 v1 Metric Geometry

Abstract

We show that there does not exist a complex d×nd\times n equiangular tight frame with d2d+1<n<d2. d^2-d+1<n<d^2. The proof, which originated from an internal model at OpenAI, mimics the relationship between real equiangular tight frames and strongly regular graphs.

Cite

@article{arxiv.2605.28738,
  title  = {The Singer-Zauner gap for equiangular tight frames},
  author = {Matthew Fickus and John Jasper and Dustin G. Mixon},
  journal= {arXiv preprint arXiv:2605.28738},
  year   = {2026}
}
R2 v1 2026-07-22T07:37:41.223Z