[r-t] Methods as polyhedra
King, Peter R
peter.king at imperial.ac.uk
Mon Apr 21 15:52:20 UTC 2008
Sorry I've been busy so it has taken to get back. Of course, I never
said the polyhedron has to exist in 3 dimensions. In fact I don't think
it can, I think the minimum for what I had in mind is 4D, which I think
alters the argument. However, I still haven't made my mind up as to
whether or not this representation is useful!
> -----Original Message-----
> From: ringing-theory-bounces at bellringers.net
> [mailto:ringing-theory-bounces at bellringers.net] On Behalf Of
> Mark Davies
> Sent: 09 April 2008 21:14
> To: ringing-theory at bellringers.net
> Subject: [r-t] Methods as polyhedra
>
> Ah! Just thought. Of course if we are looking at nodes rather
> than leads,
> then things are different.
>
> Two leads are the same - a call on one will elicit the same
> transformation
> as the same call on the other. But two nodes are not the
> same. Instead,
> nodes fall in to categories: the nodes from say W->H have a
> different set of
> transformations to the nodes from M->W.
>
> Effectively, a restriction such as "tenors together" adds an
> asymmetry to
> the search space network, and means we must map to a
> polyhedron with a
> similar asymmetry. In particular, a vertex-transitive
> polyhedron is no good,
> because all the vertices are certainly not the same. We would
> need to find a
> polyhedron with n different classes of vertices, where n
> equals the number
> of node types.
>
> So that is something very different, and I suppose Mr King
> might be right
> that we can find them... still assuming edges do not cross.
> How we actually
> go about that is another matter.
>
> MBD
>
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