论文标题
按程度序列渐近枚举
Asymptotic enumeration of hypergraphs by degree sequence
论文作者
论文摘要
我们证明了一个具有给定度序列的$ K $均匀超图的渐近公式，用于广泛的参数。特别是，我们发现一个渐近的公式等于$ n $顶点上的$ d $ g $均匀的超图，但前提是，对于常数$ c> 0 $的$ dn \ le c \ le c \ binom {n} {k} $对几乎独立二项式随机变量的简单模型的超图，从而扩展了由于第二和第三作者而导致的图形结果。
We prove an asymptotic formula for the number of $k$-uniform hypergraphs with a given degree sequence, for a wide range of parameters. In particular, we find a formula that is asymptotically equal to the number of $d$-regular $k$-uniform hypergraphs on $n$ vertices provided that $dn\le c\binom{n}{k}$ for a constant $c>0$, and $3 \leq k < n^C$ for any $C<1/9.$ Our results relate the degree sequence of a random $k$-uniform hypergraph to a simple model of nearly independent binomial random variables, thus extending the recent results for graphs due to the second and third author.
