39 citations · 46 across the 15 of their papers we have counts for
22 papers
Dimension-counting bounds for equi-isoclinic subspaces
Joseph W. Iverson, Kaysie Rose O
We make four contributions to the theory of optimal subspace packings and equi-isoclinic subspaces: (1) a new lower bound for block coherence, (2) an exact count of equi-isoclinic…
Asymmetric SICs over finite fields
Joseph W. Iverson, Dustin G. Mixon
Zauner's conjecture concerns the existence of equiangular lines in ; such a system of lines is known as a SIC. In this paper, we construct infinitely many new S…
More on the optimal arrangement of lines in
Joseph W. Iverson, John Jasper, Dustin G. Mixon
We introduce a new infinite family of equiangular tight frames. Many matrices in this family consist of two circulant blocks. We conjecture that such equia…
Totally symmetric Grassmannian codes
Matthew Fickus, Joseph W. Iverson, John Jasper +1
We introduce a general technique to construct tight fusion frames with prescribed symmetries. Applying this technique with a prescription for "all the symmetries", we construct a n…
Radon-Hurwitz Grassmannian codes
Matthew Fickus, Enrique Gomez-Leos, Joseph W. Iverson
Every equi-isoclinic tight fusion frame (EITFF) is a type of optimal code in a Grassmannian, consisting of subspaces of a finite-dimensional Hilbert space for which the smallest pr…
Towards a bilipschitz invariant theory
Jameson Cahill, Joseph W. Iverson, Dustin G. Mixon
Consider the quotient of a Hilbert space by a subgroup of its automorphisms. We study whether this orbit space can be embedded into a Hilbert space by a bilipschitz map, and we ide…
Equi-isoclinic subspaces, covers of the complete graph, and complex conference matrices
Matthew Fickus, Joseph W. Iverson, John Jasper +1
In 1992, Godsil and Hensel published a ground-breaking study of distance-regular antipodal covers of the complete graph that, among other things, introduced an important connection…
Group-invariant max filtering
Jameson Cahill, Joseph W. Iverson, Dustin G. Mixon +1
Given a real inner product space and a group of linear isometries, we construct a family of -invariant real-valued functions on that we call max filters. In the case…
Harmonic Grassmannian codes
Matthew Fickus, Joseph W. Iverson, John Jasper +1
An equi-isoclinic tight fusion frame (EITFF) is a type of Grassmannian code, being a sequence of subspaces of a finite-dimensional Hilbert space of a given dimension with the prope…
A note on tight projective 2-designs
Joseph W. Iverson, Emily J. King, Dustin G. Mixon
We study tight projective 2-designs in three different settings. In the complex setting, Zauner's conjecture predicts the existence of a tight projective 2-design in every dimensio…
Frames over finite fields: Equiangular lines in orthogonal geometry
Gary R. W. Greaves, Joseph W. Iverson, John Jasper +1
We investigate equiangular lines in finite orthogonal geometries, focusing specifically on equiangular tight frames (ETFs). In parallel with the known correspondence between real E…
Frames over finite fields: Basic theory and equiangular lines in unitary geometry
Gary R. W. Greaves, Joseph W. Iverson, John Jasper +1
We introduce the study of frames and equiangular lines in classical geometries over finite fields. After developing the basic theory, we give several examples and demonstrate finit…
Grassmannian codes from paired difference sets
Matthew Fickus, Joseph W. Iverson, John Jasper +1
An equiangular tight frame (ETF) is a sequence of vectors in a Hilbert space that achieves equality in the Welch bound and so has minimal coherence. More generally, an equichordal…
Multiplication-invariant operators and the classification of LCA group frames
Marcin Bownik, Joseph W. Iverson
In this paper we study the properties of multiplication invariant (MI) operators acting on subspaces of the vector-valued space . We characterize such operators…
Doubly transitive lines II: Almost simple symmetries
Joseph W. Iverson, Dustin G. Mixon
We study lines through the origin of finite-dimensional complex vector spaces that enjoy a doubly transitive automorphism group. This paper classifies those lines that exhibit almo…
The Zak transform and representations induced from characters of an abelian subgroup
Joseph W. Iverson
We consider a variant of the Zak transform for a finite group with respect to a fixed abelian subgroup , and demonstrate a relationship with representations of induced f…
Quantum structures from association schemes
Radhakrishnan Balu
Starting from an association scheme induced by a finite group and the corresponding Bose-Mesner algebra we construct quantum Markov chains (QMC), their entangled versions, and inte…
Doubly transitive lines I: Higman pairs and roux
Joseph W. Iverson, Dustin G. Mixon
We study lines through the origin of finite-dimensional complex vector spaces that enjoy a doubly transitive automorphism group. In doing so, we make fundamental connections with b…
Optimal line packings from finite group actions
Joseph W. Iverson, John Jasper, Dustin G. Mixon
We provide a general program for finding nice arrangements of points in real or complex projective space from transitive actions of finite groups. In many cases, these arrangements…
Optimal line packings from nonabelian groups
Joseph W. Iverson, John Jasper, Dustin G. Mixon
We use group schemes to construct optimal packings of lines through the origin. In this setting, optimal line packings are naturally characterized using representation theory, whic…
Frames generated by compact group actions
Joseph W. Iverson
Let be a compact group, and let be a representation of on a Hilbert space . We classify invariant subspaces of in terms of range function…
Subspaces of invariant under translation by an abelian subgroup
Joseph W. Iverson
For a second countable locally compact group and a closed abelian subgroup , we give a range function classification of closed subspaces in invariant under left tra…