#10527: Implementation of quiver mutation type
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Reporter: stumpc5 | Owner: sage-combinat
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.0
Component: combinatorics | Resolution:
Keywords: quiver mutation type | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Christian Stump | Merged in:
Dependencies: #10349 | Stopgaps:
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Comment (by stumpc5):
> I think !QuiverMutationType(BB,1,1) shouldn't return affine A1. They
are double edges in different senses. (Affine A1 is two arrows in the
quiver convention, while I think the only reasonable interpretation of
BB,1,1 is a double edge in the Lie convention, i.e. a valued quiver with
one edge and labels (1,2). That is to say, I think BB,1,1 should return
B2.)
What you say is right, but I am also not very convinced of returning B2: I
don't like that the BBn-1 and Bn turn into B2 for n=2, since the BB tells
that there are two special outgoing edges. (Same for CCn-1 as well.) BCn-1
turns into one edge (1,-4) which seems to be more appropriate. What about
not allowing BB1 and CC1 as input, and starting both series with n=2? We
actually do the same with BDn-1, where we start only with n=3 since one
end is special in the B sense and the other in the D sense.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10527#comment:24>
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