[r-t] 147 TDMM

[Richard Smith]

Alexander Holroyd wrote:

> Congratulations, Richard, I'm very pleased to see this come to fruition!
>
> Can you give us a list of the plans?

Probably too long to email to the list, but here it is:

   http://ex-parrot.com/~richard/minor/147/plans.txt

Methods are notated using the two-letter abbreviations given 
on John Warboy's website:

   http://website.lineone.net/~jswcomps/comp06.htm#TD

The number in parentheses after the method is the number of 
lead ends and heads -- i.e. twice the number of leads 
present in the plan.  The number of distinct rotations / 
reflections is also given (which for the mathematically 
inclined, is the index of the [inner] automorphism group in 
A_5.)

> It would be interesting if there were an automated way to analyse the plans, 
> and identify the new things.  I'm thinking of something like the following. 
> For any _two_ methods alone, the splicing theory is well understood (e.g. 
> 3-lead splices etc.).  A first step would be to weed out all those plans that 
> can be explained by any combination of such splices. Any ideas of a good way 
> to do this?

I don't immediately know how to go about this, but I think 
that going through the process partly by hand is probably 
the only way to work out a good way of automating it. 
That's what the email I've just sent out is starting to do.

Now that I've worked out how simple splicing theory relates 
to the plans found, I hope I can move on to the next level 
of complexity -- multiple simple splices (e.g. plans that 
involve a course splice and a three-lead splice, such as the 
Lightfoot six composition).

> Then all those remaining would involve grid splices and other 
> more interesting things.  A further refinement would be to tease out the 
> structure of these - e.g. identify them as "interesting splice X combined 
> with a 3-lead splice".  Any idea how to do this?

No ideas yet, but lets see if it becomes more obvious when 
I've done the next stage of the analysis.

> It would also be interesting to see if the search with singles is feasible.

Singles and extending it to the 178 are both possible 
avenues for future searching.  But right at the moment I 
think I want to concentrate on analysising what I've found 
and automating (at least parts of) the analysis.

RAS