Geodesic
Asymptotic enumeration of hypergraphs by degree sequence
Advances in Combinatorics (2022)

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arXiv
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 $C1/9.$ 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.
Publié le : 
Nina Kamčev; Anita Liebenau; Nick Wormald. Asymptotic enumeration of hypergraphs by degree sequence. Advances in Combinatorics (2022). http://geodesic.mathdoc.fr/item/ADVC_2022_a8/
@article{ADVC_2022_a8,
     author = {Nina Kam\v{c}ev and Anita Liebenau and Nick Wormald},
     title = {Asymptotic enumeration of hypergraphs by degree sequence},
     journal = {Advances in Combinatorics},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2022_a8/}
}
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