#17540: Poset.dimension
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Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-6.5
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers:
combinatorics | Work issues:
Keywords: | Commit:
Authors: | 216d59efca2e03ebce6e9fd76f150abb32e369d5
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/17540 |
Dependencies: |
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Comment (by dimpase):
Replying to [comment:15 ncohen]:
> > according to [FT00], instead of the hypergraph on `inc(P)`, it
suffices to restrict to the induced subhypergraph of the critical
incomparable pairs (see Lemma 3.3 in [loc.cit.]), and then do the same
chromatic number computation.
>
> I do not see how that would change anything. You are just telling me
that only a subset of points of the hypergraph matters, but that does not
give me the set of edges that only involve critical pairs.
It seems that you get a smaller ILP; you run your acyclicity test and
compute cycles just as you do, but only leave critical pairs there (i.e.
you take the subhypergraph induced on the critical pairs --- the edges get
intersected with the subset of critical pairs).
--
Ticket URL: <http://trac.sagemath.org/ticket/17540#comment:19>
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