4 papers
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…
Small gaps between configurations of prime polynomials
Hans Parshall
We find arbitrarily large configurations of irreducible polynomials over finite fields that are separated by low degree polynomials. Our proof adapts an argument of Pintz from the…