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math.FA2026
The Singer-Zauner gap for equiangular tight frames
Matthew Fickus, John Jasper, Dustin G. Mixon
We show that there does not exist a complex equiangular tight frame with \[ d^2-d+1<n<d^2. \] The proof, which originated from an internal model at OpenAI, mimics the r…
math.FA2025
Doubly transitive equiangular tight frames that contain regular simplices
Matthew Fickus, Evan C. Lake
An equiangular tight frame (ETF) is a finite sequence of equal norm vectors in a Hilbert space that achieves equality in the Welch bound, and so has minimal coherence. The binder o…