[r-t] Stedmonster triples

[Alexander E Holroyd]

For a concrete question (among others): is there an extent entirely in 
whole 10s?  I.e. of the form

504*(x A)

where each A is either 5.1.5.1.5.1.5.1.5 or 1.5.1.5.1.5.1.5.1 and each x 
is any place notation (but preferably in a way that doesn't produce long 
places).

I would think there must be...

On 07-May-20 1:50 AM, Richard Pullin wrote:
> On Tue 5 May 2020, Ander Holroyd wrote:
> 
>  >This is the analogue of Stedman, but with alternate quick and slow 10s
>  >and 4-pull dodges in 67:
> 
>  >http://www.boojum.org.uk/cgi-bin/line.pl?bells=7&pn=7.1.5.1.>>5.1.5.1.5.1.7.5.1.5.1.5.1.5.1.5&title=Stedmonster%20Triples&style=1&place-bellsx=on&rule=1%2C10&layout=1&action.x=1 <http://www.boojum.org.uk/cgi-bin/line.pl?bells=7&pn=7.1.5.1.5.1.5.1.5.1.7.5.1.5.1.5.1.5.1.5&title=Stedmonster%20Triples&style=1&place-bellsx=on&rule=1%2C10&layout=1&action.x=1>
> 
> 
> Three of these blocks of 10 changes can between them contain the 30 
> cosets required for an extent based on the 168 group. A block of three 
> 10s wouldn't really work in Stedmonster, as you'd end up with a slow 10 
> course end and therefore wouldn't have looped back to the starting 
> point. But you could come up with a block of two 10s (Block A) and a 
> separate block of 10 in the Erin equivalent of Stedmonster (Block B). 
> For fun I called this method "Monsterin."
> This would then be the basis for a peal of spliced containing exactly 
> 2/3 Stedmonster and 1/3 Monsterin.
> 
> For Block A you can start the Stedmonster with a full quick 10 and a 
> bob, and then ring a plain slow 10. This block of 20 changes produces 
> 2316574, one of the part ends from our group of 168. For Block B, start 
> with 1523647 and ring a plain 10 of Monsterin. This contains the 
> remaining 10 cosets needed, and produces 5314276 at the 10-end. When we 
> compare 5314276 back to 1523647 we find that it is a transfigure of one 
> of our part ends, so we have successfully looped back to the start of 
> Block B.
> 
> So if there was a way of joining Block B to Block A with a pair of 
> singles, not only would we have the full part of 30 changes, but Block B 
> would also be the means to joining up all 168 parts. You could single-in 
> the Block B at will to shunt between parts, and also have the bonus of 
> some full courses of Monsterin between pairs of singles. There are a 
> couple of spliced Stedman & Erin peals that use this idea.
> 
> There are a few ways of joining up Blocks A and B using weird internal 
> singles, but they were all so horribly crass that I didn't bother 
> completing a 5040. However, Blocks A and B might still open up a good 
> avenue for elegant peals that are less directly on the 168-course plan.
> 
> Instead of producing a poor peal of spliced, I used the blocks and a few 
> adjustments to come up with quite a nice principle. The plain course 
> doesn't contain pure triples changes throughout, but this at least means 
> that the principle probably hasn't already been generated by a computer 
> search.
> It still has a strong Stedmonster basis, with lots of dodges in 6-7.
> 
> 5040 New Triples Principle
> s1,s3,s7    1652743
> (s3),s7      1367425
> s3              1352476
> 8-part, omitting (s3) from parts 4 and 8.
> Plain:   7.1.345.1.5.1.5.1.7.5.1.5.1.5.1.7.1.7.1.5.3.1.5.1.345.1.5.1.5.1
> Single: 12345 in lieu of final 1
> 
> _______________________________________________
> ringing-theory mailing list
> ringing-theory at bellringers.org
> https://bellringers.org/listinfo/ringing-theory
>