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Hypergraph regularity method is a powerful tool in [[extremal graph theory]] that refers to the combined application of hypergraph regularity lemma and associated counting lemma. It is a generalization of graph regularity method, which refers to the use of [[Szemerédi regularity lemma|Szemerédi's regularity]] and counting lemmas.
Very informally, hypergraph regularity lemma decomposes any given <math> k </math>-uniform [[hypergraph]] into random-like object with bounded parts (with an appropriate boundedness and randomness notions) that is usually easier to work with. On the other hand, hypergraph counting lemma estimates the number of hypergraphs of given isomorphism class in some collections of the random-like parts. This is an extension of Szemerédi's regularity lemma that decomposes any given graph into pseudorandom blocks, namely <math> \varepsilon </math>-regular pairs, and graph counting lemma that estimates number of copies of a fixed graph as a subgraph of a larger graph.
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