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arXiv · 2008.07757

Asymptotic enumeration of hypergraphs by degree sequence

Nina Kamčev·Anita Liebenau·Nick Wormald
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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 $dn\le c\binom{n}{k}$ 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.

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Nina Kamčev, Anita Liebenau, Nick Wormald. 2022-01-31. Asymptotic enumeration of hypergraphs by degree sequence. https://doi.org/10.19086/aic.32357

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