12 citations · 22 across the 11 of their papers we have counts for
7 papers · 1 filter
Globally optimizing small codes in real projective spaces
Dustin G. Mixon, Hans Parshall
For , we classify arrangements of points in for which the minimum distance is as large as possible. To do so, we leverage ideas from matrix…
Linear programming bounds for cliques in Paley graphs
Mark Magsino, Dustin G. Mixon, Hans Parshall
The Lovász theta number is a semidefinite programming bound on the clique number of (the complement of) a given graph. Given a vertex-transitive graph, every vertex belongs to a ma…
Small unit-distance graphs in the plane
Aidan Globus, Hans Parshall
We prove that a graph on up to 9 vertices is a unit-distance graph if and only if it does not contain one of 74 so-called minimal forbidden graphs. This extends the work of Chilaka…
Kesten-McKay law for random subensembles of Paley equiangular tight frames
Mark Magsino, Dustin G. Mixon, Hans Parshall
We apply the method of moments to prove a recent conjecture of Haikin, Zamir and Gavish (2017) concerning the distribution of the singular values of random subensembles of Paley eq…
The optimal packing of eight points in the real projective plane
Dustin G. Mixon, Hans Parshall
How can we arrange lines through the origin in three-dimensional Euclidean space in a way that maximizes the minimum interior angle between pairs of lines? Conway, Hardin and S…
A Delsarte-Style Proof of the Bukh-Cox Bound
Mark Magsino, Dustin G. Mixon, Hans Parshall
The line packing problem is concerned with the optimal packing of points in real or complex projective space so that the minimum distance between points is maximized. Until recentl…