[r-t] Bobs only Erin Triples (was: Composition search)

[Graham John]

Matthew Frye wrote:

> I remember as a teenager trying to do bobs only half-extents of bob minor
by hand (via Q-sets), and found two unique: WHW*3 obviously, and a rather
nice one that can be written WFFWFFWBBIIBBII (allergy warning: contains 65s
in this rotation). I presumed the second of these is previously known but I
don’t remember ever seeing anyone else calling or discussing it? Is anyone
able to confirm, firstly if that second one is (widely?) known, and
secondly if these are the only two possible (up to rotation/reversal).

There are 26, excluding rotations.

Graham

360 0 1 H II O WF I FH
360 0 1 H F FH OII OOI FH
360 0 3 H WH
360 0 1 H WH FH H WOH WIH
360 0 1 H WO WF IH OOH FH
360 0 1 H WOOH WIH WIH FH FH
360 0 1 H WOOIH OOI WF FH FH
360 0 1 I OO W WF O FH
360 0 1 IH W WF WII WO FH
360 0 1 II OI WF F WF IIH
360 0 3 II F
360 0 1 II F WF IIH OOH F
360 0 1 IIH WII WOOH F WF WF
360 0 1 IIH WOI WF WII WF WF
360 0 1 OI OO WOO FH F FH
360 0 1 OIH WOO FH FH OOH FH
360 0 1 OII OOI WF F W WF
360 0 1 OII WOIIH W WF WF FH
360 0 3 OO F
360 0 1 OO F WII WOO FH F
360 0 1 OOH WOO FH FH F WIIH
360 0 1 OOII OOIIH F FH F FH
360 0 1 OOII WF F WF F WOOII
360 0 3 W WH
360 0 1 W WOH WIH W WF WH
360 0 1 W WF WF WOH WOH WIIH

On 4 December 2015 at 18:08, Matthew Frye <matthew at frye.org.uk> wrote:

> I should really pay more attention to this list!* It seems I’m late to (at
> least) two very interesting discussions.
>
> On the bobs only extent of Erin, while I think it’s interesting to
> contemplate the most efficient computational methods of attacking the
> problem, it still seems far too large to be tractable without significant
> theory advances to help you on your way.
>
> > On 25 Nov 2015, at 13:07, Richard Smith <richard at ex-parrot.com> wrote:
> >
> > I've long felt that the theory of Q-sets is a special case of a more
> general theory of linkage.
>
>
> I agree. I did start thinking about such things a few years ago, but
> abandoned it as I spent more time and brainpower on my PhD work. However,
> that is finishing in a few months, and I certainly intend to look at that
> sort of idea again. As I remember, I started with the simplest cases on 3
> and 4 bells and frankly didn’t get very far at that time!
>
> In any case bobs-only Erin Triples would probably be an end-point to a
> long project, so I did get to thinking about more realistic targets on
> smaller numbers of bells. Two easier (though possibly still too difficult)
> cases that I thought might be interesting are: A. covering the complete
> space of plain bob minor with different sets of calls; has this even been
> done for just ordinary bobs and singles?** Many more opportunities with
> exotic calls, maybe including variable hunt calls. B. MUG minor, which was
> discussed in the very earliest days of the list (
> http://bellringers.net/pipermail/ringing-theory_bellringers.net/2004-September/006265.html
> ) and seems to be structurally similar to Erin, for which I don’t think a
> truly satisfactory answer was reached (I think all offered compositions
> still had half-lead calls, or multiple types of call).
>
> MF
>
> * Incidentally, apologies to those involved for somewhat disappearing
> partway through the rules/decisions discussions earlier in the year, my
> work got busy and the sheer volume of correspondence was too much to keep
> on top of.)
>
> ** I remember as a teenager trying to do bobs only half-extents of bob
> minor by hand (via Q-sets), and found two unique: WHW*3 obviously, and a
> rather nice one that can be written WFFWFFWBBIIBBII (allergy warning:
> contains 65s in this rotation). I presumed the second of these is
> previously known but I don’t remember ever seeing anyone else calling or
> discussing it? Is anyone able to confirm, firstly if that second one is
> (widely?) known, and secondly if these are the only two possible (up to
> rotation/reversal).
>
> _______________________________________________
> ringing-theory mailing list
> ringing-theory at bellringers.net
> http://bellringers.net/mailman/listinfo/ringing-theory_bellringers.net
>
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