28 citations · 270 across the 43 of their papers we have counts for
4 papers · 1 filter
All Prime Knots Through 10 Crossings Have Superbridge Index
Clayton Shonkwiler
This paper gives new upper bounds on the stick numbers of the knots , , , , , , , , , , an…
Three proofs of the Benedetto-Fickus theorem
Dustin G. Mixon, Tom Needham, Clayton Shonkwiler +1
In 2003, Benedetto and Fickus introduced a vivid intuition for an objective function called the frame potential, whose global minimizers are fundamental objects known today as unit…
Toric Symplectic Geometry and Full Spark Frames
Tom Needham, Clayton Shonkwiler
The collection of complex matrices with prescribed column norms and prescribed (nonzero) singular values forms a compact algebraic variety, which we refer to as a fram…
Admissibility and Frame Homotopy for Quaternionic Frames
Tom Needham, Clayton Shonkwiler
We consider the following questions: when do there exist quaternionic frames with given frame spectrum and given frame vector norms? When such frames exist, is it always possible t…