On Mon, 2018-01-15 at 23:28 +0200, Jori Mäntysalo wrote:
> On Mon, 15 Jan 2018, Victor Porton wrote:
>
> > I need to enumerate all labeled (that is NOT up-to-isomorphism)
> posets of N
> > elements.
> > The algorithm is here: https://stackoverflow.com/a/48270680/856090
>
> No, that paper gives "method to construct pairwise non-isomorphic
> posets",
> i.e. up-to-isomorphism.
>
> Btw, just extending poset by adding a new maximal element covering
> all
> possible subsets of maximal elements will give you all posets having
> 1, 2,
> ..., n as a linear extension. That is not enought?
Yes, you are right, that algorithm generated not all posets (not up-
to-isomorphism).
I have deleted the wrong answer at StackOverflow.
So as for now, the best solution I have is to enumerate posets up to
isomorphism and compose them with all permutations of the set of N
elements. It may generate duplicates however and thus isn't very
efficient.
I confess that I am not ready to write this code into Sage core. I will
write my own function which will use permutations to enumerate all
posets of N elements, to use in my own endeavor.
> --
> Jori Mäntysalo
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