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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.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…
math.CO2024
Totally symmetric Grassmannian codes
Matthew Fickus, Joseph W. Iverson, John Jasper +1
We introduce a general technique to construct tight fusion frames with prescribed symmetries. Applying this technique with a prescription for "all the symmetries", we construct a n…