More on hypergraph enumeration..

Gordon Royle gordon at
Thu Mar 18 07:29:53 CET 2004

I have now located the 4-uniform hypergraphs on OEIS.

They are sequence A051240 which has the name "Pure 3-dimensional 
simplicial complexes on n unlabeled nodes". Again, I am not surprised 
that you didn't find this when looking for 4-uniform hypergraphs!

There is a question "Is this the same sequence as A003189?" which is 
called "Number of 3-plexes" which has its own comment about possibly 
being an erroneous version of A051240.

The answer to that question is yes - they are meant to be the same 
sequence, but Palmer did make a mistake in his calculations of 
n-plexes; he referred to the mistake in a Maths Review review of 
another paper called "Hypergraph Enumeration".

The associated "triangle" of numbers of k-uniform hypergraphs on n 
nodes does not appear to be in OEIS...


On 15/03/2004, at 12:45 PM, Edwin Clark wrote:

> Has anyone enumerated k-uniform hypergraphs with m edges on n
> vertices (up to isomorphism) for small values of k, m and n.
> For k = 2, I know it has been done, since these are ordinary graphs, 
> but
> what about for k > 2. Say for k = 3, m = 3,4 or 5. I cannot find 
> anything in
> the OEIS.
> Maybe I'm not looking for the right words?
> --Edwin Clark

More information about the SeqFan mailing list