论文标题
极端数量的表面
The extremal number of surfaces
论文作者
论文摘要
1973年，Brown，Erdős和Sós证明，如果$ \ Mathcal {h} $是$ N $顶点上的3均匀超图，它不包含球体的三角剖分，那么$ \ Mathcal {h} $最多具有$ o（N^{5/2}）$ EDGE，并且是最好的选择。解决了一系列的猜想，也由Keevash，Long，Narayanan和Scott重申，我们表明，相同的结果适用于三角形的三角形。此外，我们将结果扩展到每个可定向的表面$ \ Mathcal {s} $。
In 1973, Brown, Erdős and Sós proved that if $\mathcal{H}$ is a 3-uniform hypergraph on $n$ vertices which contains no triangulation of the sphere, then $\mathcal{H}$ has at most $O(n^{5/2})$ edges, and this bound is the best possible up to a constant factor. Resolving a conjecture of Linial, also reiterated by Keevash, Long, Narayanan, and Scott, we show that the same result holds for triangulations of the torus. Furthermore, we extend our result to every closed orientable surface $\mathcal{S}$.
