#19184: HigmanSims design
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Reporter: | Owner:
ncohen | Status: new
Type: | Milestone: sage-6.9
enhancement | Resolution:
Priority: major | Merged in:
Component: graph | Reviewers:
theory | Work issues:
Keywords: | Commit:
Authors: | 4bef48511f3612777591089530dbcb274886321b
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
public/19184 |
Dependencies: |
#19133 |
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Comment (by dimpase):
A polarity of a symmetric design is simply an automorphism p of order 2 of
the incidence graph, which maps points to blocks. A point P is called
absolute if P lies in the block p(P).
Once you know p with all points absolute, you can reorder points and
blocks in the way that the incidence matrix has all 1s on the diagonal,
and this is essentially the adj.mat. of the graph you are after.
Now, how does one go about finding polarites? Construct the incidence
graph, compute its automorphism group a, find representatives of the
conjugacy classes of a, select these which have representatives of order
2, mapping points to blocks. In this case there will be just two such
class representatives, so you need to pick one, p, with all points
absolute.
Let me know if you get stuck...
--
Ticket URL: <http://trac.sagemath.org/ticket/19184#comment:2>
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