[r-t] Extension question

[Philip Saddleton]

Don Morrison wrote:
> I'm afraid however many times I look at the Decision on method
> extension I can never really get my head around it. I just don't
> have proper model of what it's trying to do; to me it ends up being
> just a bunch of nearly inscrutable tables.
>
> Anyway, my current confusion is "How do alliance methods extend?",
> particularly with respect to "What's the relationship between the
> treble's path ins the parent and the child?" I suspect this can all be
> deduced from the Decision itself, but I fear I'm not capable of
> working it out. Can anyone help?
>
> To be a little more specific
>
> - a relatively normal alliance method, with the usual palindromic
>   symmetry, the treble the only principle hunt, and it leading full
>   across the lead end
>
> - the treble's path extends all the way to the back; that is, this is
>   not a little method
>
> - at stage 2N it dodges in positions {p1-p2, p3-p4, ... pm-pn}, and
>   hunts through the other dodging positions
>
> At stage 2N+2 what does it's path look like? Does the extended path
> have an extra dodge, or an extra hunt compared to the lower stage? And
> where does it go? Anywhere we like? Is the extended treble path
> unique, or are there multiple possible treble paths for various
> different possible extensions?
>   
There are multiple possibilities (assuming of course that works above 
and below the treble can be found that meet the additional requirements.
> What happens if instead of every dodging position being filled by a
> dodge or a hunt, the last one is cat's ears? Presumably the last one
> has to remain cat's ears, or is something else possible?
>
>   
It has to remain cat's ears.
> What if it's got a path such as that in Eskimo Blue Day, with an
> unusual dodging position? Does the dodge stay put, shift, or have
> another, presumably unusual one, added to it?
>   
Any of the above.
> What if it's got a really goofy treble path like Easton Neston Supreme
> or Kalymnos?
>
>   
Basically, a section of the path that looks like a plain or treble 
dodging path can extend in the same way. I think that if the treble 
revisits a place within a half-lead after moving two or more places away 
then there is no extension path (by two stages, at least) involving 
repetition of this section.

I have never been happy about the way that the Decision is defined by 
example. What is needed is a general way of extending place notation, 
along with any necessary restrictions for particular classes of methods. 
I am working on this.

Philip