Document Type
Article
Publication Date
3-2018
Abstract
An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. Though they arise in many applications, only a few methods for constructing them are known. Motivated by the connection between real ETFs and graph theory, we introduce the notion of ETFs that are symmetric about their centroid. We then discuss how well-known constructions, such as harmonic ETFs and Steiner ETFs, can have centroidal symmetry. Finally, we establish a new equivalence between centroid-symmetric real ETFs and certain types of strongly regular graphs (SRGs). Together, these results give the first proof of the existence of certain SRGs, as well as the disproofs of the existence of others.
DOI
10.1016/j.acha.2016.06.004
Source Publication
Applied and Computational Harmonic Analysis
Recommended Citation
Fickus, M. C., Jasper, J., Mixon, D. G., Peterson, J. D., & Watson, C. E. (2018). Equiangular tight frames with centroidal symmetry. Applied and Computational Harmonic Analysis, 44(2), 476–496. https://doi.org/10.1016/j.acha.2016.06.004
Comments
This post contains the e-print version sourced from arXiv:1509.04059 [math.FA];
Date of arXiv submission: 14 Sep 2015, updated 20 June 2016 [version 2].
The publisher's digital version of record for this article is hosted at ScienceDirect. A digital subscription to Applied and Computational Harmonic Analysis is required to access the full text of the final article. A citation is noted below.