Exact solution of the hypergraph Turán problem for k-uniform linear paths

  title={Exact solution of the hypergraph Tur{\'a}n problem for k-uniform linear paths},
  author={Zolt{\'a}n F{\"u}redi and Tao Jiang and Robert Seiver},
A k-uniform linear path of length ℓ, denoted by ℙℓ(k), is a family of k-sets {F1,...,Fℓ such that |Fi ∩ Fi+1|=1 for each i and Fi ∩ Fbj = $\not 0$ whenever |i−j|>1. Given a k-uniform hypergraph H and a positive integer n, the k-uniform hypergraph Turán number of H, denoted by exk(n, H), is the maximum number of edges in a k-uniform hypergraph $\mathcal{F}$ on n vertices that does not contain H as a subhypergraph. With an intensive use of the delta-system method, we determine exk(n, Pℓ(k… 
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