[Nauty] Computing inequivalent preorders on $n$ points for $n > 7$

[Brendan McKay]

Hi Mark,

The most efficient method is given in this paper:

https://cs.uwaterloo.ca/journals/JIS/VOL8/McKay/mckay170.pdf

Although the topologies were not made constructively for that study,
the method is explicit and efficient and could work up to 16 points.

But, to focus on small sizes, you need to implement the bijection
between topologies and transitive digraphs that have a loop on
every vertex.  I forgot how to run our fast poset generator so I
made them up to 9 points by a slower method (in a few minutes).

I will send you the transitive digraphs off-list.

Brendan.

On 19/11/19 3:20 pm, Mark Bowron wrote:
> About a year ago I wrote a very simple C program that, after running for
> about three days on a Macbook Pro, produces a list of representatives from
> each of the 4535 distinct isomorphism classes of preorders (finite
> topologies) on 7 points.  I posted this list and other similar ones (in
> text files) at:
>
> https://www.mathtransit.com/finite_topological_spaces.php
>
> Has anyone yet produced a list of the 35979 inequivalent preorders on 8
> points?  Is any known algorithm fast enough to accomplish this task within
> a reasonable amount of time, say a few weeks, on a Macbook Pro?  Or better
> still, might such a list be publicly available somewhere?
>
> Thank you in advance for any info on this specific topic.
>
> Mark Bowron
>