[r-t] Challenge

[Robert Bennett]

	It would be nice to have all the different false course
combinations and sets of courses for those combinations. Should be
easy for someone on this site. It is probably already in some
textbook of group theory if someone could translate it into the terms
the rest of us understand. 

	Usually start by transposing all the FCHs by the inverse of the other
FCHs. Doing this with the BDK FCHs, you get 35264, 56342, 64523,
42635, 23456.  

	  

	For Cambridge Major, the one worked out by GBT in his book is the 24
course, 3 part one. (I think - I can't find the copy I used to
have). Middleton's 25 course block comes out if you use the
same process in a different order. 

As noted, there are often lots of special features in most methods,
clean leads like the M-W lead of Cambridge, special courses like
In/5ths For London. It would be nice to have them on a website, or in
a book somewhere. 
----- Original Message -----
 From:ringing-theory at bellringers.net
To:
Cc:
Sent:Tue, 30 Apr 2013 11:27:04 +0100
Subject:[r-t] Challenge

Hi All,

Talk of sets of true leads reminded me that there was something of the

sort in Giles B Thompson's 'Compleat Cambridge' (1997). The method 
mentioned by John Goldthorpe and Glenn Taylor is discussed but perhaps

the best description of its concept is the analogy GBT gives:

Consider Chess. A Knight threatens eight squares. How many Knights can

be placed on a board so none threatens any other? Well, 64/8 = 8 but 
this is not right. A Knight threatens squares of the opposite colour
so 
the answer is 32. As ringers, we happily say that a 'cps' method is
true 
if singles are not used.

GBT then quotes an article at RW62/838 by Gordon Halls and Denis 
Carlisle. Inter alia they show that falseness of Group D (32546,
46253) 
leads to a group of permitted course heads generated by 64523 -- if
one 
occurs, all may occur. Obviously, courses rather than leads were used
in 
1962 since it was the best that could be done at the time with this 
technique give the size of the problem, but it would be interesting to

see the groups of permitted leads for the methods currently in
question.

If an extent is required, the word 'permitted' becomes 'required'.

Just a thought.

Robin
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