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

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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 : 
@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 Combinatronics},
     publisher = {mathdoc},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2022_a8/}
}
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AU  - Nick Wormald
TI  - Asymptotic enumeration of hypergraphs by degree sequence
JO  - Advances in Combinatronics
PY  - 2022
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADVC_2022_a8/
LA  - en
ID  - ADVC_2022_a8
ER  - 
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%A Anita Liebenau
%A Nick Wormald
%T Asymptotic enumeration of hypergraphs by degree sequence
%J Advances in Combinatronics
%D 2022
%I mathdoc
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%G en
%F ADVC_2022_a8
Nina Kamčev; Anita Liebenau; Nick Wormald. Asymptotic enumeration of hypergraphs by degree sequence. Advances in Combinatronics (2022). http://geodesic.mathdoc.fr/item/ADVC_2022_a8/