#18484: Implement k-chordality of a matroid
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Reporter: Rudi | Owner:
Type: enhancement | Status: needs_info
Priority: minor | Milestone: sage-6.8
Component: matroid theory | Resolution:
Keywords: chord | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/matroids/k_chordal-18484 | 6f9e8633781d3843c59d8b89e333b1844c090880
Dependencies: | Stopgaps:
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Comment (by tscrim):
Here's how you can generate large chordal matroids:
{{{
sage: W = WeylGroup(['A',5]) # increase this integer
sage: w0 = W.long_element()
sage: mat = matrix([x.to_vector() for x in
w0.inversions(inversion_type='roots')])
sage: M = Matroid(mat.transpose())
sage: M.chordality()
4
}}}
It's a theorem (I think due to Stanley, but I could be wrong) that all
inversion arrangements of root systems of type A are chordal.
I have seen that Bonin paper, however his notion of k-chordal is opposite
of what I'm interested in (and actually the original definition I gave)
and does not (generally) recover the original notion of chordal. However
if we add an upper bound parameter, we can support Bonin's definition as
well. I will add this.
I'm not quite sure what you mean by this:
> Efficiency will not be a reason to not give that positive review.
I'd take the code which is more efficient. However I think checking for a
frozenset being in the ''frozenset'' `circuits` as containment is
(amortized) O(1) and we have to generate all circuits anyways...well at
least for `chordality`. I'm not sure that testing for closures would be
faster as circuits are generally relatively small. Will you be running
timings between the two codes or do you want me to?
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Ticket URL: <http://trac.sagemath.org/ticket/18484#comment:14>
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