More on the optimal arrangement of $2d$ lines in $\mathbb{C}^d$

Dustin G. Mixon; John Jasper; Joseph W. Iverson

More on the optimal arrangement of $2d$ lines in $\mathbb{C}^d$

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arxiv 2410.17379 v1 pith:XJGRXHID submitted 2024-10-22 math.MG math.COmath.FA

Joseph W. Iverson , John Jasper , Dustin G. Mixon This is my paper · ORCID

classification math.MGmath.COmath.FA

keywords conjectureequiangularfamilyframestighttimesadditionapplication

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abstract

We introduce a new infinite family of $d\times 2d$ equiangular tight frames. Many matrices in this family consist of two $d\times d$ circulant blocks. We conjecture that such equiangular tight frames exist for every $d$. We show that our conjecture holds for $d\leq 165$ by a computer-assisted application of a Newton-Kantorovich theorem. In addition, we supply numerical constructions that corroborate our conjecture for $d\leq 1500$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Abelian and Dihedral equiangular tight frames of redundancy $2$
math.CO 2025-09 conditional novelty 7.0 of 10

Every regular dihedral equiangular tight frame of redundancy 2 is genuinely projective and corresponds exactly to a 2-negacirculant skew Hadamard matrix.
Recovering a group from few orbits
math.RT 2024-11 conditional novelty 7.0 of 10

One generic complex orbit determines a finite linear symmetry group up to isomorphism; two generic real orbits suffice, and concrete recovery needs an orbit count governed by representation multiplicities.

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