In this paper, we study r-uniform hypergraphs H without cycles of length less than five, employing the definition of a hypergraph cycle due to Berge. In particular, for r = 3, we show that if H has n vertices and a maximum number of edges, then |H| = 1 6 n + o(n). This also asymptotically determines the generalized Turán number T3(n, 8, 4). Some results are based on our bounds for the maximum s...

We give a construction of set $$A \subset \mathbb N$$ such that any subset $${A' A}$$ with $$|A'| \gg |A|^{2/3}$$ is neither an additive nor multiplicative Sidon set. In doing so, we refute conjecture Klurman and Pohoata.

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