#19499: Mathon's graphs on 784 vertices
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Reporter: dimpase | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.10
Component: graph theory | Resolution:
Keywords: | Merged in:
Authors: Dima Pasechnik | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/dimpase/mathon784 | 6c7e85187a0d695ef3856b83d08eaaa0520f1fc0
Dependencies: | Stopgaps:
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Comment (by dimpase):
Replying to [comment:11 ncohen]:
> > it'd actually be just one function,
`EllipticLinesProjectivePlaneScheme`, for
`mathon_pseudocylcic_merging_graph` creates a (s.r.) graph, and functions
creating srg's from stuff are normally in graphs modules...
>
> HMmmm... Not always: it seems that there is a quite close relationship
between association schemes and strongly regular graphs, so it may well be
a AssociationScheme.associated_graph or something. Could definitely be
there. It is actually better to store a function like that inan
association scheme module, for I personally don't understand it (as a
graph guy) and somebody who understand association schemes would
understand it.
as you can claim a bit of understanding of strongly regular graphs, you
can say you understand a bit of assoc. schemes with 2 classes, too :-)
>
> > For me, creating such a module would be a commitment to make it proper
(for I know all too well what should be there), and I have too many of
these already...
> > (Unless you feel an itch to partake, and in this case I'd go ahead
with this...)
>
> I can move the function there for you if you prefer. I don't take this
as a commitment for anything: I barely know what an association scheme is,
and every time I read the definition all I could think of is "who in their
right minds would define something so contrained"?
well, given that the complementary pair of s.r.graphs is an association
scheme
with 2 classes, I don't quite follow your last comment :-)
It took off when people wanted to use orbitals to study permutation
groups. Orbitals of a permutation group (0-1 matrices specifying the
partition of the set of 2-tuples induced by the group action) define an
object called, variously, coherent configuration, coherent algebra...
Restricting to transitive groups, one has homogeneous coherent
configurations, a.k.a. (non-commutative) association schemes. And then in
several important cases one gets commutativity of these matrices, and thus
the (usual) association schemes.
A bit later coding theorists wanted to use algebra to study codes, which
are special kinds of cliques in Hamming (or Johnson) graphs.
But the distance k graphs, for all, k, of these graphs also form
association scheme...
And so this was born...
--
Ticket URL: <http://trac.sagemath.org/ticket/19499#comment:12>
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