#19279: IncidenceStructure.is_generalized_quadrangle
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Reporter: ncohen | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.9
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Nathann Cohen | Work issues:
Report Upstream: N/A | Commit:
Branch: u/ncohen/19279 | 4f8a84b8f65b917883e46e28b8942ae52dd09b3d
Dependencies: #19277 | Stopgaps:
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Comment (by dimpase):
1) GQs don't necessary admit parameters; e.g.
{{{
o----o----o
| | |
o----o----o
}}}
is a GQ with 6 points and 5 lines, of which 2 are of size 3, and 3 of size
2.
(or you can take the dual, and get 5 points and 6 lines, all lines of the
same size, 2, but points incident to different number of lines).
Admittedly this is a somewhat degenerate case, where either all lines have
size 2, or all points are incident to exactly 2 lines; otherwise one
indeed has uniformity.
2) the incidence graph is bipartite, and thus must have even girth (equal
to 8, to get a GQ).
--
Ticket URL: <http://trac.sagemath.org/ticket/19279#comment:4>
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