#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 ncohen):
> as you can claim a bit of understanding of strongly regular graphs,
Ahahah. I wouldn't claim that. Neither with strongly regular graphs, nor
with combinatorial designs. I know the extent of what I don't know on
these topics.. `:-P`
> 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...
HMmmmmm... Thank you for this historical view `:-)`
About this patch: needs_work, needs_review?
Nathann
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Ticket URL: <http://trac.sagemath.org/ticket/19499#comment:13>
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