English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

An equiangular tight frame (ETF) is a sequence of unit-norm vectors in aEuclidean space whose coherence achieves equality in the Welch bound, and thusyields an optimal packing in a projective space. A regular simplex is a simpletype of ETF in which the number of vectors is one more than the dimension ofthe underlying space. More sophisticated examples include harmonic ETFs whichequate to difference sets in finite abelian groups. Recently, it was shown thatsome harmonic ETFs are comprised of regular simplices. In this paper, wecontinue the investigation into these special harmonic ETFs. We begin bycharacterizing when the subspaces that are spanned by the ETF's regularsimplices form an equi-isoclinic tight fusion frame (EITFF), which is a type ofoptimal packing in a Grassmannian space. We shall see that every difference setthat produces an EITFF in this way also yields a complex circulant conferencematrix. Next, we consider a subclass of these difference sets that can befactored in terms of a smaller difference set and a relative difference set. Itturns out that these relative difference sets lend themselves to a second,related and yet distinct, construction of complex circulant conferencematrices. Finally, we provide explicit infinite families of ETFs to which thistheory applies.

Harmonic equiangular tight frames comprised of regular simplices