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Counting substructures III: quadruple systems
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Counting substructures III: quadruple systems
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For various quadruple systems F, we give asymptotically sharp lower bounds on the number of copies of F in a quadruple system with a prescribed number of vertices and edges. Our results extend those of Furedi, Keevash, Pikhurko, Simonovits and Sudakov who proved under the same conditions that there is one copy of $F$. Our proofs use the hypergraph removal Lemma and stability results for the corresponding Turan problem proved by the above authors.
Forward citations
Cited by 2 Pith papers
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Strong counterexamples to Mubayi's supersaturation conjecture in every uniformity
Constructs stable non-r-partite r-graphs F disproving Mubayi's local supersaturation conjecture by an arbitrary constant factor K in every uniformity.
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Strong counterexamples to Mubayi's supersaturation conjecture in every uniformity
Constructs counterexamples to Mubayi's supersaturation conjecture showing the conjectured lower bound fails by arbitrary factors at q=1 for r-graphs of every uniformity.
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