  Equiangular tight frames (ETFs) may be used to construct examples of feasible
points for semidefinite programs arising in sum-of-squares (SOS) optimization.
We show how generalizing the calculations in a recent work of the authors' that
explored this connection also yields new bounds on the sparsity of (both real
and complex) ETFs. One corollary shows that Steiner ETFs corresponding to
finite projective planes are optimally sparse in the sense of achieving
tightness in a matrix inequality controlling overlaps between sparsity patterns
of distinct rows of the synthesis matrix. We also formulate several natural
open problems concerning further generalizations of our technique.
