论文标题
几乎最大直径的复合物
Complexes of nearly maximum diameter
论文作者
论文摘要
固定连接的$ D $二维简单复合物的直径是其双图的直径。我们提供了$ d $ d $二维的简单复合物，具有直径$（\ frac {1} {d \ cdot d！} - （\ log n）^{ - ε}）n^d $。直到一阶术语，这是$ n $ vertices上$ d $ complex的最大直径的最佳下限，这是一个简单的卷参数，表明$ d $ d $ d $ - d $ - 二维的简单复合物的直径最多是$ \ frac {1} {d} {d} {d} {d} \ binom {n} n} d} $。我们还找到了合适的一阶渐近线，用于$ n $ VERTICES上的$ d $ -pseudomanifold的最大直径。
The diameter of a strongly connected $d$-dimensional simplicial complex is the diameter of its dual graph. We provide a probabilistic proof of the existence of $d$-dimensional simplicial complexes with diameter $ (\frac{1}{d \cdot d!} - (\log n)^{-ε}) n^d$. Up to the first order term, this is the best possible lower bound for the maximum diameter of a $d$-complex on $n$ vertices as a simple volume argument shows that the diameter of a $d$-dimensional simplicial complex is at most $ \frac{1}{d} \binom{n}{d}$. We also find the right first-order asymptotics for the maximum diameter of a $d$-pseudomanifold on $n$ vertices.
