论文标题
稀疏超图的变性turán密度II：解决各种均匀性的棕色 - 埃德斯 - sós问题的解决方案
Degenerate Turán densities of sparse hypergraphs II: a solution to the Brown-Erdős-Sós problem for every uniformity
论文作者
论文摘要
对于固定的整数，$ r \ ge 3，e \ ge 3 $和$ v \ ge r+1 $，让$ f_r（n，v，e）$表示$ n $ n $ vertex $ r $ r $ r $ robiform-ry.-robily hypergraph中的最大边数，其中任意$ e $ un's of tunary $ e $ e $至少包含$ v+v+1 $ $ vertices。 In 1973, Brown, Erdős and Sós proved that $f_r(n,er-(e-1)k,e)=Θ(n^k)$ and conjectured that the limit $\lim_{n\rightarrow\infty}\frac{f_3(n,e+2,e)}{n^2}$ always exists for all fixed integers $e\ge 3$. In 2020 Shangguan and Tamo conjectured that the limit $\lim_{n\rightarrow\infty}\frac{f_r(n,er-(e-1)k,e)}{n^k}$ always exists for all fixed integers $r>k\ge 2$ and $e\ge 3$, which contains the BES conjecture as a special case for $r=3, k=2$.最近，基于格洛克，乔斯，金，库恩，莉切夫和皮克赫科，德尔考特和邮政的结果证明了BES猜想。扩展其结果，我们表明$ \ lim_ {n \ rightArrow \ infty} \ frac {f_r（n，er-2（e-1），e），e）} {n^2} $始终存在，从而证明了每个均匀性的bes bes bes bes bes bes bes bes bes bes bes。
For fixed integers $r\ge 3, e\ge 3$, and $v\ge r+1$, let $f_r(n,v,e)$ denote the maximum number of edges in an $n$-vertex $r$-uniform hypergraph in which the union of arbitrary $e$ distinct edges contains at least $v+1$ vertices. In 1973, Brown, Erdős and Sós proved that $f_r(n,er-(e-1)k,e)=Θ(n^k)$ and conjectured that the limit $\lim_{n\rightarrow\infty}\frac{f_3(n,e+2,e)}{n^2}$ always exists for all fixed integers $e\ge 3$. In 2020 Shangguan and Tamo conjectured that the limit $\lim_{n\rightarrow\infty}\frac{f_r(n,er-(e-1)k,e)}{n^k}$ always exists for all fixed integers $r>k\ge 2$ and $e\ge 3$, which contains the BES conjecture as a special case for $r=3, k=2$. Recently, based on a result of Glock, Joos, Kim, Kühn, Lichev, and Pikhurko, Delcourt and Postle proved the BES conjecture. Extending their result, we show that the limit $\lim_{n\rightarrow\infty}\frac{f_r(n,er-2(e-1),e)}{n^2}$ always exists, thereby proving the BES conjecture for every uniformity.
