[r-t] ringing the Mathieu group
edward.w.martin at gmail.com
Tue May 3 06:57:48 UTC 2011
On 30 April 2011 23:29, Wyld Family e-mail <wyld at waitrose.com> wrote:
> I have two suggestions for the caters problem. Both are based on
> organising the required changes in to courses of original and linking them
> together using 5ths place calls (bobs). In the first I suggest joining,
> alternately, forward and backward hunting courses with a 5ths place i.e.
> repeated 8 times. This joins together 18 courses leaving an even number to
> be introduced by Q sets of 5ths place bobs. There are 18 Q sets that can
> not be bobbed having been used in the basic block but that leaves at least 8
> routes into the courses affected.
> I don't think this will work
My reasoning is that because any block of Plain Hunt could be expressed in
either its coursing order or the reverse of its coursing order then the
above two blocks could be expressed as having c.o.
6-8-9-7-5-3-1-2-4 and 6-8-9-7-4-5-3-1-2
This suggests the need for blocks with c.o.
6-8-9-7-2-4-5-3-1 and 6-8-9-7-1-2-4-5-3
6-8-9-7-3-1-2-4-5 and 6-8-9-7-5-3-1-2-4
In which case the first and third blocks will repeat and the true extent
cannot be set out in mutually exclusive blocks of this structure.
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