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math.CO2026
Long-range expanders: construction and cutoff
Dylan J. Altschuler
Long-range expansion is a combinatorial graph property introduced to construct metric spaces with strong quantitative obstructions to low-distortion embeddings. Such extremal const…
math.CO2026
Online Beck--Fiala Down to Logarithmic Sparsity
Dylan J. Altschuler, Konstantin Tikhomirov
The Beck--Fiala conjecture asserts that every matrix with at most nonzero entries in each column has discrepancy . A major breakthrough re…