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- W3182821399 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 {it $k$-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 $ntoinfty$ 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.
- W3182821399 created "2021-07-19" @default.
- W3182821399 creator A5077565006 @default.
- W3182821399 date "2021-07-10" @default.
- W3182821399 modified "2023-09-27" @default.
- W3182821399 title "On the number of linear multipartite hypergraphs with given size" @default.
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- W3182821399 doi "https://doi.org/10.48550/arxiv.2107.04950" @default.
- W3182821399 hasPublicationYear "2021" @default.
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