110 citations · 134 across the 11 of their papers we have counts for
13 papers
Equations for the overlaps of a SIC
Len Bos, Shayne Waldron
We give a holomorphic quartic polynomial in the overlap variables whose zeros on the torus are precisely the Weyl-Heisenberg SICs (symmetric informationally complete positive opera…
Complex spherical designs from group orbits
Mozhgan Mohammadpour, Shayne Waldron
We consider the general question of when all orbits under the unitary action of a finite group give a complex spherical design. Those orbits which have large stabilisers are then g…
On Waldron Interpolation on a Simplex in
Len Bos, Sione Ma'u, Shayne Waldron
We introduce explicit families of good interpolation points for interpolation on a triangle in that may be used for either polynomial interpolation or a certain rati…
Testing isomorphism between tuples of subspaces
Emily J. King, Dustin G. Mixon, Shayne Waldron
Given two tuples of subspaces, can you tell whether the tuples are isomorphic? We develop theory and algorithms to address this fundamental question. We focus on isomorphisms in wh…
A variational characterisation of projective spherical designs over the quaternions
Shayne Waldron
We give an inequality on the packing of vectors/lines in quaternionic Hilbert space $\Hd$, which generalises those of Sidelnikov and Welch for unit vectors in $\Rd$ and $\Cd$. This…
Multivariate Lagrange interpolation and polynomials of one quaternionic variable
Shayne Waldron
This paper considers the extension of classical Lagrange interpolation in one real or complex variable to "polynomials of one quaternionic variable". To do this we develop some asp…