[r-t] Shipway Minor

[Matthew Frye]

On 12 Jun 2014, at 06:11, Alexander Holroyd <holroyd at math.ubc.ca> wrote:
> In particular, there seems to be a belief that it is impossible to get an extent without "disrupting the front work".  If I remember correctly, exactly this assertion was made in the RW when it was named in 1993. (Perhaps someone with easy access to back issues could check this).
> 
> However, this belief turns out to be wrong!  I have recently found an extent that does not disrupt the front work -- see below.  It uses 3 different types of calls, but they are the nicest 3 one could hope for: Stedman Triples type bobs and singles, and a Stedman Doubles type single in the middle of an eight (henceforth called an extreme).  Moreover, the density of calls is not at all unreasonable (for a "problem method").

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?

I haven't really managed to come up with a very good model of how to rigorously think structurally about putting together extents of either of those methods. The standard Q-set picture we would use for most plain methods is obviously a failure here, but what it can be replaced with or if it could be extended(!) is not clear. The obvious route of picking a set of mutually true divisions (usually trivial) and trying to link them up (usually seemingly impossible) is an unsatisfying basis because of the sheer number ways to choose the first part (possibly on the order of the number of particles in the universe).

I find this rather frustrating.

> The extent has some quite strange properties.  The two extremes in the part at first look like a Q-set, since they come in two "complementary" eights, with the hunting order on the front and the bells in 56 reversed. However, they aren't.  We leave an eight with an extreme, but rejoin it in the same place at an eight-end (and vice versa).  Not really sure why this works.

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.

An analogy would be Grandsire Triples without single using 5ths place calls, if you just throw in a whole Q-set of them, it doesn't help you much, you have to use them in a more unusual way to break the Q-set rules.

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.

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?

I don't expect it would be too difficult. I would be entirely unsurprised if it is something that has been composed before as a curiosity and is currently sitting in a pile of papers in a draw, forgotten.

MF