#14283: M22 graph constructor
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Reporter: ncohen | Owner: tbd
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.9
Component: graph theory | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Nathann Cohen | Merged in:
Dependencies: 14271 | Stopgaps:
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Comment (by dimpase):
A much better way is to create these 77 blocks by applying the Mathieu
group M_22 to one block, directly.
Replace {{{s= [long long boring list]}}} by
{{{
s = MathieuGroup(22)._gap_().Orbit([1,2,3,7,10,20],"OnSets").sage()
}}}
This is a bit unfortunate that one needs to write such an ugly call,
instead of just {{{MathieuGroup(22).orbit([1,2,3,7,10,20],"OnSets")}}}.
IMHO it's worth opening a ticket and fixing this, i.e. adding
{{{"OnSets"}}} and other GAP options to the orbit method.
PS. How does one find the block? Well, take the pointwise stabilizer of 3
points, say, 1, 2, 3 in {{{MathieuGroup(22)}}} and compute its orbits on
the 22 points the group acts naturally. Such a stabilizer is the
stabilizer of two points, 1 and 2, in the projective plane of order 4
induced on 2,3,...,22. There is unique like on 1 and 2 in this plane, so
you'll see an orbit of length 3 that you need to add to 1, 2, 3 to get the
block (this is the unique block on the 3 points 1, 2, 3).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14283#comment:2>
Sage <http://www.sagemath.org>
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