#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 | c26038e543830f388cdceafb139d33e5f28359cd
Dependencies: #19277 | Stopgaps:
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Comment (by dimpase):
I am telling you that Wikipedia definition has inconsistencies. E.g. it
says that by definition a GQ is a polar space of rank 2, and on the link
to polar spaces is does not give you a definition of polar space of rank
2. As well I am telling you that Wikipedia definition is by far not the
only one common in the literature.
E.g., page 200 of [BCN] says:
More generally, a generalized n-gon is a partial linear space (P,E) with
the property
that the incidence graph has diameter n and any two vertices x,y at
distance
i < n have c_j(x,y) = 1. It is said to be of order (s,t) if all of its
lines have size s + 1 and all of its points are incident to exactly t + 1
lines.
[BCN]:
https://drive.google.com/file/d/0B92yb82dH00zZWFJdkNsQm5nZmM/view?usp=sharing
Indeed, in Ghent they might burn you at stake if you try to insist on this
definition, but they have been trying to monopolise this industry for
years :-)
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Ticket URL: <http://trac.sagemath.org/ticket/19279#comment:14>
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