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De Silva, Heysse and Young determined $ex_2(K_{n_1, \\ldots, n_r}, kK_2)$ and De Silva, Heysse, Kapilow, Schenfisch and Young determined $ex_2(K_{n_1, \\ldots, n_r},kK_r)$. In this paper, as a generalization of these results, we consider three Tur\\'{a}n-type problems for $k$ disjoint cliques in $r$-partite $s$-uniform hypergraphs. 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Liu, Jian Wang","submitted_at":"2019-08-16T14:17:20Z","abstract_excerpt":"For two $s$-uniform hypergraphs $H$ and $F$, the Tur\\'{a}n number $ex_s(H,F)$ is the maximum number of edges in an $F$-free subgraph of $H$. Let $s, r, k, n_1, \\ldots, n_r$ be integers satisfying $2\\leq s\\leq r$ and $n_1\\leq n_2\\leq \\cdots\\leq n_r$. De Silva, Heysse and Young determined $ex_2(K_{n_1, \\ldots, n_r}, kK_2)$ and De Silva, Heysse, Kapilow, Schenfisch and Young determined $ex_2(K_{n_1, \\ldots, n_r},kK_r)$. In this paper, as a generalization of these results, we consider three Tur\\'{a}n-type problems for $k$ disjoint cliques in $r$-partite $s$-uniform hypergraphs. 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