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 finite sequence of equal norm vectorsin a Hilbert space of lesser dimension that achieves equality in the Welchbound and so has minimal coherence. The binder of an ETF is the set of allsubsets of its indices whose corresponding vectors form a regular simplex. AnETF achieves equality in Donoho and Elad's spark bound if and only if itsbinder is nonempty. When this occurs, its binder is the set of all linearlydependent subsets of it of minimal size. Moreover, if members of the binderform a balanced incomplete block design (BIBD) then its incidence matrix can bephased to produce a sparse representation of its dual (Naimark complement). Afew infinite families of ETFs are known to have this remarkable property. Inthis paper, we relate this property to the recently introduced concept of adoubly transitive equiangular tight frame (DTETF), namely an ETF for which thenatural action of its symmetry group is doubly transitive. In particular, weshow that the binder of any DTETF is either empty or forms a BIBD, and moreoverthat when the latter occurs, any member of the binder of its dual is an oval ofthis BIBD. We then apply this general theory to certain known infinite familiesof DTETFs. Specifically, any symplectic form on a finite vector space yields aDTETF, and we compute the binder of it and its dual, showing that the former isempty except in a single notable case, and that the latter consists of affineLagrangian subspaces; this unifies and generalizes several results from theexisting literature. We then consider the binders of four infinite families ofDTETFs that arise from quadratic forms over the field of two elements, showingthat two of these are empty except in a finite number of cases, whereas theother two form BIBDs that relate to each other, and to Lagrangian subspaces, innonobvious ways.

Doubly transitive equiangular tight frames that contain regular simplices