8 papers
Primitive sets and von Mangoldt chains: ErdÅs Problem #1196 and beyond
Boris Alexeev, Kevin Barreto, Yanyang Li +5
A set of integers is primitive if no number in the set divides another. We introduce a new method for bounding ErdÅs sums of primitive sets, suggested from output of GPT-5.4 Pro,…
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…
On the clustering behavior of sliding windows
Boris Alexeev, Wenyan Luo, Dustin G. Mixon +1
Things can go spectacularly wrong when clustering timeseries data that has been preprocessed with a sliding window. We highlight three surprising failures that emerge depending on…