[r-t] Bobs only Erin Triples (was: Composition search)

[Fred Bone]

On 24 November 2015 at 20:07, Alan Burlison said:

> On 24/11/2015 19:28, Philip Saddleton wrote:
> 
> > There is no need to do this - in a bobs only composition it is only
> > necessary to compare the last four bells at each six end.
> 
> I'm not sure what you mean by "six end" but being able to reduce the
> number of comparisons sounds good :-)

The method comes in units of six rows, commonly referred to as "sixes". 
The difference between plain and bob is at the transition between two 
sixes, i.e. at the end of one and the start of another: hence "six end".

The point of what Philip says is that for any given four bells in 4th to 
7th place, the six rows are uniquely determined (ignoring order of 
occurrence). The rows making up the six are alternately odd and even 
permutations (of rounds). The last row will be even, and the six will 
contain all 3 even permutations having the given 4 bells in the given 
places, plus all 3 odd permutations having them swapped in pairs. For 
example, the six ending in xxx4567 will contain all of 1234567, 2314567, 
3124567, plus 1325476, 2135476 and 3215476 - in some order.