Extremal t-intersecting families for direct products
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math.CO
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intersectingdirectfamiliesproductsextremalassumingcertainconditions
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In this paper, by shifting technique we study $t$-intersecting families for direct products where the ground set is divided into several parts. Assuming the size of each part is sufficiently large, we determine all extremal $t$-intersecting families for direct products. We also prove that every largest $t$-intersecting subfamily of a more general family introduced by Katona is trivial under certain conditions.
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