#18347: implement the shard intersection order on permutations
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Reporter: | Owner:
chapoton | Status: needs_work
Type: | Milestone: sage-6.7
enhancement | Resolution:
Priority: minor | Merged in:
Component: | Reviewers:
combinatorics | Work issues:
Keywords: poset | Commit:
Authors: | 878ed3a0794d123c46d7cb9ea48ad93ca2d07348
Frédéric Chapoton | Stopgaps:
Report Upstream: N/A |
Branch: |
u/chapoton/18347 |
Dependencies: |
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Comment (by vdelecroix):
Replying to [comment:21 chapoton]:
> Well. I did implement this just to compute the number of maximal chains
and the mobius
> numbers. So only the "abstract" poset was needed. But of course, this is
more useful to other people if the vertices of the poset are more or less
labelled by permutations.
>
> I do not think nevertheless that it is necessary to have the elements be
permutations.
>
> So I am happy with the current state of things..
I see. Could you mention somewhere (probably in the docstring of
`ShardPosetElement` and `ShardPoset`) that the elements are '''not'''
permutation (for computational reasons). But hopefully they are easily
recovered:
{{{
sage: P = posets.ShardPoset(4)
sage: mins = P.minimal_elements()[0]
sage: p = Permutation(mins)
[2, 3, 4, 1]
sage: p.decreasing_runs()
[[2], [3], [4, 1]]
}}}
(or a more relevant example)
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/18347#comment:22>
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