Hypergraph Turán Numbers of Vertex Disjoint Cycles

The Turán number of a k-uniform hypergraph H, denoted by exk(n;H), is the maximum number of edges in any k-uniform hypergraph F on n vertices which does not contain H as a subgraph. Let Cℓ(k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal C}_\ell ^{(k)}$$\end{document} denote the family of all k-uniform minimal cycles of length ℓ, S(ℓ1,⋯,ℓr)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal S}({\ell _1}, \cdots ,{\ell _r})$$\end{document} denote the family of hypergraphs consisting of unions of r vertex disjoint minimal cycles of length ℓ1,…,ℓr, respectively, and ℂℓ(k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{C}_\ell ^{(k)}$$\end{document} denote a k-uniform linear cycle of length ℓ. We determine precisely exk(n;S(ℓ1,⋯,ℓr))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e{x_k}\left( {n;{\cal S}({\ell _1}, \cdots ,{\ell _r})} \right)$$\end{document} and exk(n;ℂℓ1(k),…,ℂℓr(k))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e{x_k}\left( {n;\mathbb{C}_{{\ell _1}}^{(k)}, \ldots ,\mathbb{C}_{{\ell _r}}^{(k)}} \right)$$\end{document} for sufficiently large n. Our results extend recent results of Füredi and Jiang who determined the Turán numbers for single k-uniform minimal cycles and linear cycles.