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math.CO2024
Limits of sparse hypergraphs
Riley Thornton
We generalize ultraproducts and local-global limits of graphs to hypergraphs and other structures. We show that the local statistics of an ultraproduct of a sequence of hypergraphs…
math.CO2024
Factor of iid colorings of trees
Riley Thornton
We show that, for every , the 4-regular tree has an fiid 4-coloring where a given vertex is assigned the 4th color with probability at most . We also construct 5-colorings…