[r-t] New method - Auryn Differential Minor
Alexander Holroyd
holroyd at math.ubc.ca
Tue Dec 4 19:09:05 UTC 2012
Hi Eddie,
Yes, I agree - the two "problems" of asymmetry and strange parity
actuually work together here so that truth is achieved. I still find it
miraculous that it all works out though. (Of course if one considers the
original description as a differential method it is not miraculous).
Ander
On Tue, 4 Dec 2012, edward martin wrote:
> On 3 December 2012 20:07, Alexander Holroyd <holroyd at math.ubc.ca> wrote:
>
>> . The problem with -25- is that the parity of the
>> rows for the section are +-+-, so the two rows with the treble in 3rds are
>> the same parity. The proof I know that the standard calling works requires
>> paity structure +--+ or ++-- in each section.
>
> This is the case if the method is symmetric but need not be so if asymmetric
> eg
> the first half lead gives the rows
> 231645 +
> 326154 -
> 321654 +
> 236145 -
> had the method been symmetric, the second half would give
> 456123 -
> 541632 +
> 546132 -
> 451623 +
> which would be hard to deal with, however, the asymmetric second half
> gives the rows
> 426153 +
> 241635 -
> 246135 +
> 421653 -
> and that aspect no longer exists.
>
> Having the same half-lead rows and the same full-lead rows, whether 34
> x 34 versus x 34 x in the sections when treble is in 5-6 or in 12
> actually gives the same rows but in different sequence, so the
> asymmetric method looks promising from that point of view
>
> Eddie
>
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