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math.CO2025
Averages of hypergraphs and higher arity stability
Artem Chernikov, Henry Towsner
We show that -ary functions giving the measure of the intersection of multi-parametric families of sets in probability spaces, e.g. $(x,y,z) \in X \times Y \times Z \mapsto μ(P_…
math.CO2024
Intersecting sets in probability spaces and Shelah's classification
Artem Chernikov, Henry Towsner
For and , given a sufficiently long sequence of events in a probability space all of measure at least , some of them will have…
math.CO2024
Perfect stable regularity lemma and slice-wise stable hypergraphs
Artem Chernikov, Henry Towsner
We investigate various forms of (model-theoretic) stability for hypergraphs and their corresponding strengthenings of the hypergraph regularity lemma with respect to partitions of…