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

Fri Dec 4 19:07:24 UTC 2015

> There are 26, excluding rotations.

I think that there are 140. I made a list once, but lost it long ago.  
Luckily the internet archive to the rescue!

https://web.archive.org/web/20050426201814/http://www-users.cs.york.ac.uk/~ianb/solid/plainbobminorbobs.text

Ian

P.S. There could well be errors in the list below - it's been a long time..

360 bbpbbpbpbppbbpbppbbppbbpbbpppp
360 bbpbbppbbppbpbbppbpbpbbpbbpppp
360 bbpbbppppbbpbbpbpbppbbpbppbbpp
360 bbpbbppppbbpbbppbbppbpbbppbpbp
360 bbpbpbppbbpbppbbppbbpbbppppbbp
360 bbpbppbbppbbpbbppppbbpbbpbpbpp
360 bbpbppbbppbpbppppbbpppbpbbpppp
360 bbpbpppbbppppbpbppbbppbpbbpppp
360 bbppbbpbbppppbbpbbpbpbppbbpbpp
360 bbppbbppbpbbppbpbpbbpbbppppbbp
360 bbppbpbbppbpbpbbpbbppppbbpbbpp
360 bbppbpbbppppbbpbpppbbppppbpbpp
360 bbppbpbpbbpbbppppbbpbbppbbppbp
360 bbppbpbppppbbpppbpbbppppbbpbpp
360 bbpppbpbbppppbbpbppbbppbpbpppp
360 bbpppbppppbbpppbppppbbpppbpppp
360 bbppppbbpbbpbpbppbbpbppbbppbbp
360 bbppppbbpbbppbbppbpbbppbpbpbbp
360 bbppppbbpbppbbppbpbppppbbpppbp
360 bbppppbbpbpppbbppppbpbppbbppbp
360 bbppppbpbppbbppbpbbppppbbpbppp
360 bbppppbpppbbppppbpppbbppppbppp
360 bpbbpbbppppbbpbbppbbppbpbbppbp
360 bpbbpbpbppbbpbppbbppbbpbbppppb
360 bpbbppbbppbpbbppbpbpbbpbbppppb
360 bpbbppbpbpbbpbbppppbbpbbppbbpp
360 bpbbppppbbpbbpbpbppbbpbppbbppb
360 bpbbppppbbpbbppbbppbpbbppbpbpb
360 bpbbppppbbpbppbbppbpbppppbbppp
360 bpbbppppbbpbpppbbppppbpbppbbpp
360 bpbpbbpbbppppbbpbbppbbppbpbbpp
360 bpbpbppbbpbppbbppbbpbbppppbbpb
360 bpbppbbpbppbbppbbpbbppppbbpbbp
360 bpbppbbppbbpbbppppbbpbbpbpbppb
360 bpbppbbppbpbbppppbbpbpppbbpppp
360 bpbppbbppbpbppppbbpppbpbbppppb
360 bpbpppbbppppbpbppbbppbpbbppppb
360 bpbppppbbpppbpbbppppbbpbppbbpp
360 bppbbpbbppppbbpbbpbpbppbbpbppb
360 bppbbpbppbbppbbpbbppppbbpbbpbp
360 bppbbppbbpbbppppbbpbbpbpbppbbp
360 bppbbppbpbbppbpbpbbpbbppppbbpb
360 bppbbppbpbbppppbbpbpppbbppppbp
360 bppbbppbpbppppbbpppbpbbppppbbp
360 bppbpbbppbpbpbbpbbppppbbpbbppb
360 bppbpbbppppbbpbpppbbppppbpbppb
360 bppbpbpbbpbbppppbbpbbppbbppbpb
360 bppbpbppppbbpppbpbbppppbbpbppb
360 bpppbbppppbpbppbbppbpbbppppbbp
360 bpppbbppppbpppbbppppbpppbbpppp
360 bpppbpbbppppbbpbppbbppbpbppppb
360 bpppbppppbbpppbppppbbpppbppppb
360 bppppbbpbbpbpbppbbpbppbbppbbpb
360 bppppbbpbbppbbppbpbbppbpbpbbpb
360 bppppbbpbppbbppbpbppppbbpppbpb
360 bppppbbpbpppbbppppbpbppbbppbpb
360 bppppbbpppbpbbppppbbpbppbbppbp
360 bppppbbpppbppppbbpppbppppbbppp
360 bppppbpbppbbppbpbbppppbbpbpppb
360 bppppbpppbbppppbpppbbppppbpppb
360 pbbpbbpbpbppbbpbppbbppbbpbbppp
360 pbbpbbppbbppbpbbppbpbpbbpbbppp
360 pbbpbbppppbbpbbpbpbppbbpbppbbp
360 pbbpbbppppbbpbbppbbppbpbbppbpb
360 pbbpbpbppbbpbppbbppbbpbbppppbb
360 pbbpbppbbppbbpbbppppbbpbbpbpbp
360 pbbpbppbbppbpbppppbbpppbpbbppp
360 pbbpbpppbbppppbpbppbbppbpbbppp
360 pbbppbbpbbppppbbpbbpbpbppbbpbp
360 pbbppbbppbpbbppbpbpbbpbbppppbb
360 pbbppbpbbppbpbpbbpbbppppbbpbbp
360 pbbppbpbbppppbbpbpppbbppppbpbp
360 pbbppbpbpbbpbbppppbbpbbppbbppb
360 pbbppbpbppppbbpppbpbbppppbbpbp
360 pbbpppbpbbppppbbpbppbbppbpbppp
360 pbbpppbppppbbpppbppppbbpppbppp
360 pbbppppbbpbbpbpbppbbpbppbbppbb
360 pbbppppbbpbbppbbppbpbbppbpbpbb
360 pbbppppbbpbppbbppbpbppppbbpppb
360 pbbppppbbpbpppbbppppbpbppbbppb
360 pbbppppbpbppbbppbpbbppppbbpbpp
360 pbbppppbpppbbppppbpppbbppppbpp
360 pbpbbpbbppppbbpbbppbbppbpbbppb
360 pbpbbppbpbpbbpbbppppbbpbbppbbp
360 pbpbbppppbbpbppbbppbpbppppbbpp
360 pbpbbppppbbpbpppbbppppbpbppbbp
360 pbpbpbbpbbppppbbpbbppbbppbpbbp
360 pbpbppbbpbppbbppbbpbbppppbbpbb
360 pbpbppbbppbpbbppppbbpbpppbbppp
360 pbpbppppbbpppbpbbppppbbpbppbbp
360 pbppbbpbppbbppbbpbbppppbbpbbpb
360 pbppbbppbbpbbppppbbpbbpbpbppbb
360 pbppbbppbpbbppppbbpbpppbbppppb
360 pbppbbppbpbppppbbpppbpbbppppbb
360 pbpppbbppppbpbppbbppbpbbppppbb
360 pbpppbbppppbpppbbppppbpppbbppp
360 pbppppbbpppbpbbppppbbpbppbbppb
360 pbppppbbpppbppppbbpppbppppbbpp
360 ppbbpbbpbpbppbbpbppbbppbbpbbpp
360 ppbbpbbppbbppbpbbppbpbpbbpbbpp
360 ppbbpbbppppbbpbbpbpbppbbpbppbb
360 ppbbpbppbbppbbpbbppppbbpbbpbpb
360 ppbbpbppbbppbpbppppbbpppbpbbpp
360 ppbbpbpppbbppppbpbppbbppbpbbpp
360 ppbbppbbpbbppppbbpbbpbpbppbbpb
360 ppbbppbpbbppbpbpbbpbbppppbbpbb
360 ppbbppbpbbppppbbpbpppbbppppbpb
360 ppbbppbpbppppbbpppbpbbppppbbpb
360 ppbbpppbpbbppppbbpbppbbppbpbpp
360 ppbbpppbppppbbpppbppppbbpppbpp
360 ppbbppppbpbppbbppbpbbppppbbpbp
360 ppbbppppbpppbbppppbpppbbppppbp
360 ppbpbbppbpbpbbpbbppppbbpbbppbb
360 ppbpbbppppbbpbppbbppbpbppppbbp
360 ppbpbbppppbbpbpppbbppppbpbppbb
360 ppbpbpbbpbbppppbbpbbppbbppbpbb
360 ppbpbppbbppbpbbppppbbpbpppbbpp
360 ppbpbppppbbpppbpbbppppbbpbppbb
360 ppbpppbbppppbpppbbppppbpppbbpp
360 ppbppppbbpppbppppbbpppbppppbbp
360 pppbbpbbpbpbppbbpbppbbppbbpbbp
360 pppbbpbbppbbppbpbbppbpbpbbpbbp
360 pppbbpbppbbppbpbppppbbpppbpbbp
360 pppbbpbpppbbppppbpbppbbppbpbbp
360 pppbbpppbpbbppppbbpbppbbppbpbp
360 pppbbpppbppppbbpppbppppbbpppbp
360 pppbbppppbpbppbbppbpbbppppbbpb
360 pppbbppppbpppbbppppbpppbbppppb
360 pppbpbbppppbbpbppbbppbpbppppbb
360 pppbpbppbbppbpbbppppbbpbpppbbp
360 pppbpppbbppppbpppbbppppbpppbbp
360 pppbppppbbpppbppppbbpppbppppbb
360 ppppbbpbbpbpbppbbpbppbbppbbpbb
360 ppppbbpbbppbbppbpbbppbpbpbbpbb
360 ppppbbpbppbbppbpbppppbbpppbpbb
360 ppppbbpbpppbbppppbpbppbbppbpbb
360 ppppbbpppbpbbppppbbpbppbbppbpb
360 ppppbbpppbppppbbpppbppppbbpppb
360 ppppbpbppbbppbpbbppppbbpbpppbb
360 ppppbpppbbppppbpppbbppppbpppbb

On Fri, 04 Dec 2015 18:47:19 -0000, Graham John  
<graham at changeringing.co.uk> wrote:

> 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 FH360	0	1	H F FH OII OOI FH360	0	3	H WH360	0	1	H WH  
> FH H WOH WIH360	0	1	H WO WF IH OOH FH360	0	1	H WOOH WIH WIH FH FH 
> 360	0	1	H WOOIH OOI WF FH FH360	0	1	I OO W WF O FH360	0	1	IH W WF WII WO  
> FH360	0	1	II OI WF F WF IIH360	0	3	II F360	0	1	II F WF IIH OOH F 
> 360	0	1	IIH WII WOOH F WF WF360	0	1	IIH WOI WF WII WF WF360	0	1	OI OO  
> WOO FH F FH360	0	1	OIH WOO FH FH OOH FH360	0	1	OII OOI WF F W WF 
> 360	0	1	OII WOIIH W WF WF FH360	0	3	OO F360	0	1	OO F WII WOO FH F 
> 360	0	1	OOH WOO FH FH F WIIH360	0	1	OOII OOIIH F FH F FH360	0	1	OOII WF  
> F WF F WOOII360	0	3	W WH360	0	1	W WOH WIH W WF WH360	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
>

-- 
Ian Broster
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