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- W2855870131 abstract "A fundamental problem in pattern avoidance is describing the asymptotic behavior of the extremal function and its generalizations. We prove an equivalence between the asymptotics of the graph extremal function for a class of bipartite graphs and the asymptotics of the matrix extremal function. We use the equivalence to prove several new bounds on the extremal functions of graphs. We develop a new method to bound the extremal function of hypergraphs in terms of the extremal function of their associated multidimensional matrices, improving the bound of the extremal function of $d$-permutation hypergraphs of length $k$ from $O(n^{d-1})$ to $2^{O(k)}n^{d-1}$." @default.
- W2855870131 created "2018-07-19" @default.
- W2855870131 creator A5082420630 @default.
- W2855870131 date "2018-07-05" @default.
- W2855870131 modified "2023-09-27" @default.
- W2855870131 title "Improved bounds on the extremal function of hypergraphs." @default.
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