[r-t] Auryn

Alexander Holroyd holroyd at math.ubc.ca
Fri Dec 7 01:30:46 UTC 2012

Hi Robin,

Of course you are right that the second 34-section has the opposite parity 
to the first one, otherwise there would be no hope of a bobs-only 720. 
(By "34 section" I meant the first one).

Mike Ovenden's June 05 posting is indeed somewhat relevant here, but to my 
mind does not resolve the issue.

Mike's approach is concerned with determining whether there is a true set 
of leads (or half leads) that give the extent.  In the case of Auryn that 
is trivially the case, because of the original interpretation in terms of 
the mirror-symmetric group: two leads of Auryn is half of this group (and 
a subgroup of index 2), one lead is a quarter.  Your observation below is 
a manifestation of this.

However this does not explain why the standard calling works.  I repeat my 
challenge: are there any other TD methods with this property (standard 
calling true but no 6 mutually true courses).


On Thu, 6 Dec 2012, Robin Woolley wrote:

> Hi All,
> I suspect that Philip Earis gave the wrong link for Mike Ovenden. Whether or 
> not, Mike showed how to extract a group of required lead-heads for 
> 'difficult' methods on 18th June 2005.
> I showed Auryn to Michael Foulds who has the programs ready to hand and he 
> extracted the RLHs as {23456, 54326}. The first lead end is 45236 which when 
> followed by the given bob is precisely the only non-trivial member of the RLH 
> group. (There are a couple of negative RLHs which shouldn't matter if singles 
> are not used.)
> Just a thought.
> Robin 
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