13 citations · 14 across the 12 of their papers we have counts for
9 papers · 1 filter
Short proofs in combinatorics, probability and number theory II
Boris Alexeev, Moe Putterman, Mehtaab Sawhney +2
We give a quintet of proofs resulting from questions posed by Erdős. These questions concern ordinary lines in planar point sets, sequences with uniformly small exponential sums, $…
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…
Partisan gerrymandering with geographically compact districts
Boris Alexeev, Dustin G. Mixon
Bizarrely shaped voting districts are frequently lambasted as likely instances of gerrymandering. In order to systematically identify such instances, researchers have devised sever…
An impossibility theorem for gerrymandering
Boris Alexeev, Dustin G. Mixon
The U.S. Supreme Court is currently deliberating over whether a proposed mathematical formula should be used to detect unconstitutional partisan gerrymandering. We show that in som…
On minimal colorings without monochromatic solutions to a linear equation
Boris Alexeev, Jacob Fox, Ron Graham
For a ring R and system L of linear homogeneous equations, we call a coloring of the nonzero elements of R minimal for L if there are no monochromatic solutions to L and the colori…