# [r-t] Double extent of major

Thu Dec 6 19:08:56 UTC 2007

```Simon Humphrey said  on 05/12/2007 09:22:
>> Come to think of it, is it possible to construct a true 40.320 of
>> plain major using just bobs?
>>
> I'd be interested in seeing a proof of the answer to this.  Ander?
> I remember arguing with Denis Carlisle about it, some 30-odd years ago.  I
> had produced a 7-part 40320 of Plain Bob Major and asked him if he'd prove
> it; but he said he didn't need to because it was bound to be false.
> My feeling now is that Denis was right.  But I wonder . . . now, where did I
> put that composition . . .
> SH
>
>
The proof is precisely analogous to that for Grandsire Triples. Here's
my version:

We require to produce a cycle of all of the in-course lead heads where
each one maps to the one obtained by a plain or bobbed lead, according
to the compostion. Think of this as a permutation of the 2520 lead
heads. It is an even cycle, hence an odd permutation, A.

one in the same course. This consists of odd (7-) cycles, so is an even
permutation, B.

Now consider B followed by A. This maps each plain lead head to itself,
and each bobbed lead head to the one that would be obtained by calling a
bob a course later.

Since it is a 1-1 mapping, each bobbed lead-head must map to another
(3-) cycles, so is even. But B is even and A odd, so BA is odd.

Hence A does not exist.

--
Regards
Philip