#19184: HigmanSims design
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Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-6.9
enhancement | Resolution:
Priority: major | Merged in:
Component: graph | Reviewers:
theory | Work issues:
Keywords: | Commit:
Authors: | 848a9724b6565639b2dd182f8468782150105bdf
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
public/19184 |
Dependencies: |
#19133 |
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Comment (by dimpase):
Replying to [comment:16 ncohen]:
> > How about making code to compute polarities in !SRG_176_49_12_14()
generic, working for any symmetric design?
> > Namely, something like `is_self_polar` method for symmetric
!IncidenceStructures
> > that can in addition return the representatives of possible
polarities?
>
> I do not know half of this terminology that you use `^^;`
A 2-design is called symmetric if it has as many points as blocks, and
with the number of blocks on a point equal the block size (e.g. PG(2,q),
and, more generally, finite projective planes, are symmetric 2-designs).
The dual of a symmetric 2-design is the design with points and blocks
swapping the roles.
A symmetric 2-design is called self-dual if it is isomorphic to its dual.
A self-dual symmetric 2-design is called self-polar if it has a polarity.
OK, and for the good measure, a duality is an isomorphism between the
design and its dual. Every polarity is a duality. Dualities can be
computed in the same way as polarity (just drop order==2 requirement). So
it would also be very natural to have `is_self_dual` method.
--
Ticket URL: <http://trac.sagemath.org/ticket/19184#comment:17>
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