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- W3185898909 abstract "For any given integer $$rgeqslant 3$$ , let $$k=k(n)$$ be an integer with $$rleqslant kleqslant n$$ . A hypergraph is r-uniform if each edge is a set of r vertices, and is said to be linear if two edges intersect in at most one vertex. Let $$A_1,ldots ,A_k$$ be a given k-partition of [n] with $$|A_i|=n_igeqslant 1$$ . An r-uniform hypergraph H is called k-partite if each edge e satisfies $$|ecap A_i|leqslant 1$$ for $$1leqslant ileqslant k$$ . In this paper, the number of linear k-partite r-uniform hypergraphs on $$nrightarrow infty $$ vertices is determined asymptotically when the number of edges is $$m(n)=o(n^{frac{4}{3}})$$ . For $$k=n$$ , it is the number of linear r-uniform hypergraphs on vertex set [n] with $$m=o(n^{ frac{4}{3}})$$ edges." @default.
- W3185898909 created "2021-08-02" @default.
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- W3185898909 date "2021-07-18" @default.
- W3185898909 modified "2023-09-27" @default.
- W3185898909 title "On the Number of Linear Multipartite Hypergraphs with Given Size" @default.
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- W3185898909 doi "https://doi.org/10.1007/s00373-021-02370-1" @default.
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