I am working a 3-graph problem. I convert it to calculate Turan density, that is $lim_{n\to \infty}\frac{ex_3(n,F)}{\binom{n}{3}}$, where F is a3-graph. I'd like to know are there some methods and classic papers in this area?
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1$\begingroup$ This is a rather broad question. We are very bad at calculating Turán densities, with exact answers known for very few $F$. It might help to know a little bit about the $F$ you are interested in. $\endgroup$– Ben BarberCommented May 7, 2016 at 11:00
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$\begingroup$ @BenBarber I'm interested in tight cycles, expansion of stars and the 3-graphs viewing triangles of wheels as edges. $\endgroup$– ConnorCommented May 7, 2016 at 20:05
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In his 2011 paper Peter Keevash surveys the known results and methods, and discusses some open problems: Hypergraph Turán problems, Surveys in combinatorics 392 (2011): 83-140.
In particular, you might want to look at flag algebras. See, for instance
Falgas-Ravry, V., & Vaughan, E. R. (2013). Applications of the semi-definite method to the Turán density problem for 3-graphs. Combinatorics, Probability and Computing, 22(01), 21-54, doi:10.1017/S0963548312000508
Razborov, A. A. (2013). Flag algebras: an interim report. In The Mathematics of Paul Erdős II (pp. 207-232).
answered May 8, 2016 at 9:41