Abstract
Let α( H) be the stability number of a hypergraph H = ( X, E ). T( n, k, α) is the smallest q such that there exists a k-uniform hypergraph H with n vertices, q edges and with α( H) ⩽ α. A k-uniform hypergraph H, with n vertices, T( n, k, α) edges and α( H) ⩽α is a Turan hypergraph. The value of T( n, 2, α) is given by a theorem of Turan. In this paper new lower bounds to T( n, k, α) are obtained and it is proved that an infinity of affine spaces are Turan hypergraphs.
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