166 citations · 655 across the 82 of their papers we have counts for
17 papers · 1 filter
Short spherical -design curves
Emily J. King, Dustin G. Mixon
We study the minimum arclength of spherical -design curves, i.e., closed rectifiable curves on whose normalized arclength measure exactly integrates every polynomial of de…
Asymptotically optimal approximate Hadamard matrices
Boris Alexeev, John Jasper, Dustin G. Mixon
An approximate Hadamard matrix is a well-conditioned square matrix with all entries in . We measure the quality of a matrix by its condition number, i.e., the ratio of it…
Forbidden Sidon subsets of perfect difference sets, featuring a human-assisted proof
Boris Alexeev, Dustin G. Mixon
We resolve a $1000 Erdős prize problem, complete with formal verification generated by a large language model. In over a dozen papers, beginning in 1976 and spanning two decades, P…
The independence and clique cover numbers of the squarefree graph
Boris Alexeev, Dustin G. Mixon, Will Sawin
We determine the largest subset such that for all , the product is not squarefree. Specifically, the maximum size is achieved by the comp…
The Erdős unit distance problem for small point sets
Boris Alexeev, Dustin G. Mixon, Hans Parshall
We improve the best known upper bound on the number of edges in a unit-distance graph on vertices for each . When , our bounds match the best kn…
Compact majority-minority districts almost never exist
Boris Alexeev, Dustin G. Mixon
For a uniformly distributed population, we show that with high probability, any majority-minority voting district containing a fraction of the population necessarily exhibits a tin…