#19123: LatticePoset: add is_vertically_decomposable
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Reporter: jmantysalo | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.9
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Jori Mäntysalo | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jmantysalo/vertically_decomposable|
0d472a68c9edf4ddea1404ff0cb6d2f508de55d0
Dependencies: | Stopgaps:
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Comment (by ncohen):
> OK. What should be the name of the argument? `certificate`?
`give_me_the_list=True`?
Isn't there a terminology for those points? If it is only for lattices,
maybe you could have `return_cutvertices=True` or something?
> Except for the 2-element lattice there is one simple definition that
generalizes this:
>
> {{{
> any(P.cover_relations_graph().is_cut_vertex(e) for e in P)
> }}}
Wouldn't work for a poset on three elements, one being greater than the
two others (which are incomparable).
> If the poset has coverings `2 -> 6` and `4 -> 9`, then no element `3..8`
can be a decomposition element. After founding, say, `2 -> 6` we could
check `5 ->`, `4 ->` and so on. But after founding `4 -> 9` we should have
a somewhat complicated stack to skip re-checking biggest covers of `4` and
`5`. I guess that the algorithm would be slower in reality, but I am quite
sure that it would be better in some theoretical meaning.
HMmm... Skipping some edges without additional assumption on the order in
which they are returned? I do not know... This is not so bad, for the
moment `:-)`
Nathann
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Ticket URL: <http://trac.sagemath.org/ticket/19123#comment:7>
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