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    On Frankl and Furedi's conjecture for 3-uniform hypergraphs

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    The Lagrangian of a hypergraph has been a useful tool in hypergraph extremal problems. In most applications, we need an upper bound for the Lagrangian of a hypergraph. Frankl and Furedi in \cite{FF} conjectured that the rr-graph with mm edges formed by taking the first mm sets in the colex ordering of N(r){\mathbb N}^{(r)} has the largest Lagrangian of all rr-graphs with mm edges. In this paper, we give some partial results for this conjecture.Comment: 19 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1211.650