[r-t] 8 bell cyclic callings

Ben Willetts ben at benjw.org.uk
Fri Nov 9 18:36:31 UTC 2007

I think this follow-up message I wrote on 3 November didn't go to the group. 
My error.

I wrote:
> For those who can't be bothered to look:
> 2 calls - 2 comps (0 ending in rounds)
> 3 calls - 19 comps (14 ending in rounds)
> 4 calls - 66 comps (14 ending in rounds)
> 5 calls - 216 comps (7 ending in rounds)
> 6 calls - 2146 comps (532 ending in rounds)

I've just realised that although the script was indeed generating true 
compositions that end in a cyclic course and don't repeat any coursing 
orders, I hadn't been taking out those compositions which pass through a 
cyclic course in the middle.

For example, the five-call list included BBBBB and FMHWV, both of which end 
up in rounds.  However, BBB generates 7823456 and FMH generates 14567823, so 
the five-call versions are pretty useless for a cyclic seven-part.  The 
amended code removes these.

I've also added the option of specifying a particular start to the 
compositions, so have been able to generate figures for 7-call compositions 
and estimate those for 8-calls (I could get the exact figures but I don't 
have the enthusiasm).

The amended figures are:
2-4 calls - as above
5 calls - 206 comps (5 ending in rounds)
6 calls - 2027 comps (504 ending in rounds)
7 calls - 11,695 comps (1701 ending in rounds)
8 calls - approx 75,000 comps (approx 12,000 ending in rounds)

The generator is at  <http://www.benjw.org.uk/cgi-bin/cyclic.cgi> if anyone 
wants a play.


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