[r-t] Ringable Alternating Groups On Five Bells

Alexander Holroyd holroyd at math.ubc.ca
Sat Aug 29 17:00:17 BST 2020

A fair bit of this was discussed in 2004.  (You have to dig a bit):





On 29/08/2020 00:26, Richard Pullin wrote:
> This is really interesting and useful, thanks for sharing.
> As the alternating group on 5 is isomorphic to Hudson's group, it 
> would be interesting to see which of these blocks can be turned into 
> Hudson type components for Minor methods and principles. For example, 
> the Doubles six: can be replaced by in 
> Minor, which is a very easy-to-see demonstration of the (123) cycles 
> being replaced by (123)(456) cycles. I'm sure the idea of using A_5 in 
> this way will have occurred to others, but they may have been put off 
> by the tendency of 3/4-blow places in the resulting Minor methods.
> If you arbitrarily try this on a bobbed lead of Grandsire Doubles, one 
> result is:,2 (which perhaps closer resembles Double 
> Grandsire Doubles with bobs at the half lead and lead end.) The 
> method's plain course is Hudson's group, so the trick has worked. As 
> the half lead rows are the same as in Cambridge S and Oxford TB, you 
> can get a number of variants by replacing the half lead with 5 and/or 
> the lead head with 1. I was then reminded that one of these variants 
> had already been devised a few months ago by the mathematician Robert 
> A Wilson (though his method has the tenor as hunt bell, so I rotated it.)
> We can go a step further and turn this into a challenging Principle 
> with 360 changes in the plain course, though some might prefer to 
> think of it as a variable-treble touch of the Plain method:
> https://complib.org/method/39339?accessKey=b9d3f9ca822c8bd08bdc2248ec151b4e5c89b0 
> <https://complib.org/method/39339?accessKey=b9d3f9ca822c8bd08bdc2248ec151b4e5c89b0> For 
> a 720 you simply use two singles a course apart:
> https://complib.org/composition/70150?accessKey=4222c763a30983fab67f274873ab5552ffe14201 
> <https://complib.org/composition/70150?accessKey=4222c763a30983fab67f274873ab5552ffe14201>
> I love how this extent is analogous to a 2-single 120 of Stedman 
> Doubles, which brings us right back to the original topic of A_5.
> So what else can be done with the Doubles blocks?
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