[r-t] Stedmonster triples

[Richard Pullin]

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
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