Counting substructures III: quadruple systems

Details Counting substructures III: quadruple systems Counting substructures III: quadruple systems

2009-05-28

arxiv.org/abs/0905.4735v1

Mathematics

Combinatorics

Scientific paper

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.

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