[r-t] Extension question

[Don Morrison]

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?

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?

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?

What if it's got a really goofy treble path like Easton Neston Supreme
or Kalymnos?



-- 
Don Morrison <dfm at ringing.org>
"It was no good looking inconspicuous unless people could see that
you were being inconspicuous."
  -- Terry Pratchett, _The Amazing Maurice and his Educated Rodents_