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math.CO2025
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…
math.CO2025
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…
math.CO2025
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…