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Creators/Authors contains: "Nie, Jiaxi"

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  1. ; ; ; (, Random Structures & Algorithms)
    ABSTRACT For ak‐uniform hypergraph and a positive integer , the Ramsey number denotes the minimum such that every ‐vertex ‐free ‐uniform hypergraph contains an independent set of vertices. A hypergraph isslowly growingif there is an ordering of its edges such that for each . We prove that if is fixed and is any non‐k‐partite slowly growing ‐uniform hypergraph, then for ,In particular, we deduce that the off‐diagonal Ramsey number is of order , where is the triple system . This is the only 3‐uniform Berge triangle for which the polynomial power of its off‐diagonal Ramsey number was not previously known. Our constructions use pseudorandom graphs and hypergraph containers. 
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  2. ; (, SIAM Journal on Discrete Mathematics)
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  3. ; ; (, Graphs and Combinatorics)
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  4. ; (, Random Structures & Algorithms)
    Abstract In this paper, we consider a randomized greedy algorithm for independent sets inr‐uniformd‐regular hypergraphsGonnvertices with girthg. By analyzing the expected size of the independent sets generated by this algorithm, we show that, whereconverges to 0 asg → ∞for fixeddandr, andf(d, r) is determined by a differential equation. This extends earlier results of Garmarnik and Goldberg for graphs [8]. We also prove that when applying this algorithm to uniform linear hypergraphs with bounded degree, the size of the independent sets generated by this algorithm concentrate around the mean asymptotically almost surely. 
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