[r-t] Shipway Minor

Alexander Holroyd holroyd at math.ubc.ca
Mon Jun 16 21:49:53 UTC 2014

```On Sun, 15 Jun 2014, Matthew Frye wrote:

> Very nice! It does seem a bit of a cheat to have calls half way through
a division, IIRC there's a discussion from the very early days of this
list on MUG minor that seems very similar, with a similar result
(reasonable extent, but needed half-divsion calls). I don't suppose
anyone has come up with a proof that you *can't* do it (either Shipway or
MUG) with just the obvious (division-end) calls?

Well, don't forget that the "division" (or lead) of shipway consists of
two eights, so the Stedman Triples type calls already occur in two places
in the lead (as they do in Stedman).  So I don't know what the "obvious
calls" are, and the extremes are actually division-end calls (if you start
at a symmetry point).  So my extent actually has 5 different types of
call, although that doesn't bother me...

My own criteria for what makes a reasonable extent don't have that much to
do with the number and placement of calls.  To me it is more important
that some decent sized chunks of the plain course get rung, and that when
calls do occur they don't dirupt the method so much that it no longer
feels like ringing it.  (In Shipway I would even be willing, just, to
accept 56 places made in multiple possible places during the eight - I
started out my current investigation with a 5 part extent like that).

I'd be interested to hear other people views on what constitutes a
reasonable extent in a problem method.  I suspect there are substantial
differences.

Returning to the more specific question, indeed I do not know whether
Shipway can be done with only Stedman Triples calls, or indeed with any
two or any one of the three types of call I used (althought I think all
these are rather unlikely, and perhaps the "one call" possibilities can be
ruled out by exhaustive searches).

> Well, I'm sure you know the superficial reason it works is that it
> doesn't obviously not work, so is a perfectly valid thing to do, then
> carry on. This actually looks to me something like there's some kind of
> Q-set-like rule prohibiting the extent with just the two division-end
> calls, and a Q-set usage of these extremes doesn't solve that, so you
> need the more exotic usage that *does* break this block.
>
> I would conjecture that any such extent with these three calls must have
> at least one pair of extremes used in this way. Proof or counter-example
> would be welcome.

Of course, I too would be interested to see this!

> On 12 Jun 2014, at 13:57, Ben Waller <b.j.waller at hotmail.co.uk> wrote:

>> This is a vast improvement on the previous extent, but it has made me
>> wonder...  Is it possible to obtain a 1440 with the 'Stedman
>> Triples-type' bob and single only, or even just bobs?  i.e. Can the
>> extremes be dispensed with for an MEB?

Well, that is two different questions, of course.  I suspect a MEB is
possible with only one type of call, even _any_ call that doesn't
obviously fail for some reason.  In fact there might even be a general
theorem to that effect.

A 1440 is potentially harder.  I wouldn't be surprised if it could be done
in Shipway with fewer types of call, though.

Ander

```