[r-t] Extension

[Robin Woolley]

This may be of some interest:

Having had time to think about it, perhaps the following will be clearer on
the Alliance extension front. To make life easier, I only consider for
simple Alliance methods, just a combination of the treble hunting and
dodging.

Taking Minor as the example, the extensions allowed above the treble are AB,
BC, CD and DE; below the treble we have CD, DE, EF, FG where A,..,G means
treble in 1sts,..,6ths.

We can effectively only start an extension where the allowed extensions
above and below are the same. This means, the only allowed extensions of
Alliance Minor must start CD or DE above and below.

What most would consider Alliance methods at the six bell stage are of the
type PPT or PTT. (There must be others of course). Type PPT has dodging only
in 5-6 whilst PTT has dodging in 3-4 also. It follows that the extensions of
each type must be PPPT and PTTT. It follows also that anything of the type
PPTT at the Major stage cannot be an extension of a Minor method. Generally,
we can say that the extension of an Alliance method cannot repeat the type
of the first section or the last section.

As a last example, if the 'type-string' of an Alliance Royal method is
VWXYZ, then the type strings of the extension could be VWWXYZ, VWXXYZ or
VWXYYZ.

I personally would like to see a relaxation of the Decisions in the this
area. Now that indefinite extensions are required, the we could turn the
problem round to say that, in following the extension sequence of an
Alliance method from infinity to zero, we end up with a piece of work
occurring zero times. "The limit as n tends to, well six, in this case"

I need to search my memory about this a bit more, but Perivale Alliance is a
good example of this. The type strings at six and eight bells are of type
PPT and PPTT. Such an extension would not be allowed now BUT, speaking from
memory and this is about 5 years ago, they do make a good 'extension pair'.
The argument goes that the extension cannot be allowed as there is no work
above the treble in 5-6 at Minor and something is being introduced at Major.
I seem to recall that it extends quite nicely to higher numbers also. It is
simply made up of the repeating unit x4x3 BUT my memory could be wrong on
this since the details are not on this machine!!

A problem with Easton Neston Alliance, for example, is that it is really
stretching the concept of Alliance to its breaking point.

On Extension in general, I remark the following. My advice to my (not-so)
little boy when, in dealing with mathematics, there are two types of
difficult problem. Some are difficult per se and others are difficult
because they are tedious to solve. I'll add a third - those problems which
are easy to do, but difficult to describe accurately or simply. Extension is
one of these. In fact, the mechanical parts of the Decisions (e.g.,
(G)C2(b)(ii)) could be given in one line. That would be fun, wouldn't it?

Best wishes
Robin