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math.CO2024
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…
math.MG2024
The nerd snipers problem
Boris Alexeev, Dustin G. Mixon
We correct errors that appear throughout "The vicious neighbour problem" by Tao and Wu. We seek to solve the following problem. Suppose nerds are distributed uniformly at rando…
math.CO2024
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…