[r-t] Bobs only Erin Triples (was: Composition search)
Edmund Mottershead
edmund.mottershead at gmail.com
Mon Nov 30 13:12:26 UTC 2015
Does this rule out a three part composition straight off the bat as well?
On 29 Nov 2015 12:04, "Richard Smith" <richard at ex-parrot.com> wrote:
>
> On Sat, Nov 28, 2015 at 2:53 AM Richard Smith wrote:
>>>
>>>> If a multi-part bobs-only extent of Erin exists, then the number of
>>>> parts must be one of 168, 60, 24, 21, 20, 12, 10, 8, 7, 6, 5, 4, 3, 2 or 1.
>>>>
>>>
>>> I'm having trouble getting my head around what the part heads of a six
>>> part, bobs only extent of Erin might be; the only ones I can imagine would
>>> have a 3-cycle in them. What am I missing?
>>>
>>
>> 1234567
>> 2143756
>> 1234675
>> 2143567
>> 1234756
>> 2143675
>> 1234567
>>
>
> No. That doesn't work as it contains a single 3-cycle, c.f. 1234675.
>
> The group in question has all permutations of 123 while 456 permute in
> phase:
>
> 123456 213546 231564 321654 312645 132465
>
> Although half of the elements are of order 3 and contain 3-cycles, none
> are just a 3-cycle and so they're not immediately rule out by the falseness.
>
> A regular 12-part is a bit harder...
>>
>
> It can be done in two ways, and both need searching separately.
>
> In one, the pairs 12, 34 and 56 rotate, and swap to keep parity:
>
> 123456 345612 561234
> 124365 346521 562143
> 213465 435621 651243
> 214356 436512 652134
>
> The other has all even permutations of 1234 (which would include 3-cycle),
> together with a linked 3-cycle on 567:
>
> 1234567 1423756 3241756
> 3412567 2314756 4132756
> 1342675 2431675 4321567
> 4213675 3124675 2143567
>
> As always, Brian Price's 'Composition of Peals in Parts' provides the
> definitive guide to these things.
>
> RAS
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