More on hypergraph enumeration..
Gordon Royle
gordon at csse.uwa.edu.au
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...
Gordon
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
>
>
>
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