论文标题
Turán数量的有序紧密的超速Paths
Turán Numbers of Ordered Tight Hyperpaths
论文作者
论文摘要
订购的HyperGraph是一个HyperGraph $ G $，其顶点套装$ V（g）$是线性订购的。当$ r \ l \ le s <2r $和$ n $均匀时，我们发现$ r $ rubiform $ s $ s $ s $ s $ s $ vertex的$ s $ s $ vertex紧密路径$ p^{（r）} _ s $（带顶点）的Turán号我们的结果暗示$ \ mathrm {ex} _ {>}（n，p^{（r）} _ s）=（1- \ frac {1} {1} {2^{s-r}} + o（1））\ \ binom {n}当$ r \ ge 2s $时，$ \ mathrm {ex} _ {>}的渐近学（n，p^{（r）} _ s）$保持打开状态。对于$ r = 3 $，我们给出了$ r $ rubiform $ n $ n $ vertex HyperGraph不包含$ p^{（r）} _ s $的构造，我们认为这是渐近的极端。
An ordered hypergraph is a hypergraph $G$ whose vertex set $V(G)$ is linearly ordered. We find the Turán numbers for the $r$-uniform $s$-vertex tight path $P^{(r)}_s$ (with vertices in the natural order) exactly when $r\le s < 2r$ and $n$ is even; our results imply $\mathrm{ex}_{>}(n,P^{(r)}_s)=(1-\frac{1}{2^{s-r}} + o(1))\binom{n}{r}$ when $r\le s<2r$. When $r\ge 2s$, the asymptotics of $\mathrm{ex}_{>}(n,P^{(r)}_s)$ remain open. For $r=3$, we give a construction of an $r$-uniform $n$-vertex hypergraph not containing $P^{(r)}_s$ which we conjecture to be asymptotically extremal.
