Asymptotic enumeration of hypergraphs by degree sequence

Abstract

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 $dn\le c\left(\genfrac{}{}{0ex}{}{n}{k}\right)$ for a constant $c>0$, and $3\le k<n^C$ 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.

References in corpus (2)

• Approximate counting of regular hypergraphs
• Asymptotic enumeration of sparse uniform hypergraphs with given degrees