5 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 ErdÅs. These questions concern ordinary lines in planar point sets, sequences with uniformly small exponential sums,…
Forbidden Sidon subsets of perfect difference sets, featuring a human-assisted proof
Boris Alexeev, Dustin G. Mixon
We resolve a $1000 ErdÅs prize problem, complete with formal verification generated by a large language model. In over a dozen papers, beginning in 1976 and spanning two decades,…
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…
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 ErdÅs 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…