[r-t] Stedmonster triples

Alexander E Holroyd holroyd at math.ubc.ca
Thu May 7 13:10:49 BST 2020

Oh, wait, my composition already has that property. Never mind!

On 07-May-20 12:53 PM, Alexander E Holroyd wrote:
> 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 or 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=>> 
>> <http://www.boojum.org.uk/cgi-bin/line.pl?bells=7&pn=> 
>> 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.
>> Single: 12345 in lieu of final 1
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