[r-t] Treble place paths

[Alexander Holroyd]

As I think Richard Smith pointed out yonks ago, there is a relatively 
simple algorithm for determining whether a method like this is likely to 
yield an extent; or more precisely whether there is a set of in-course 
half-leads that constitute an extent.

There are 60 possible in-course lead heads / lead ends with the treble in 
1sts place.  Given a method, certain pairs of them will be false against 
each other.  (For normal treble-dodging minor methods they are all 
mutually true).  For these methods with 24 rows in the half lead, an 
extent requires 30 mutually true half leads.  In general there is no 
particularly easy way to find out whether sufficiently many mutually true 
blocks exist, but in this case, since 30 is exactly half of the total, it 
just amounts to testing whether the falseness graph is bipartite, which 
is easy; see
http://en.wikipedia.org/wiki/Bipartite_graph#Testing_bipartiteness

Perhaps some energetic person (e.g. one who has their own "method 
search" program...) could do a quick search of all methods with treble 
path 121123432123456543456656 to see which ones have 30 mutually true 
half-leads?

Ander


On Mon, 23 Jan 2012, Alexander Holroyd wrote:

> On Mon, 23 Jan 2012, Philip Earis wrote:
>
>> When I saw him recently Ander Holroyd mooted another attractive new elegant 
>> "pointy" path where the treble rings 8 blows in each place. This is 
>> especially nice, as it works on 6 bells and can be logically extended to 
>> any even stage:
>> 
>> 121123432123456543456656
>> 
>> Suggestions of how this (or the major etc equivalents) can be best 
>> exploited would be very welcome.
>
> A while ago I looked into minor methods where the treble triple-dodoges in 
> each place that can produce the extent.  I wasn't able to find anything 
> particularly good, but one example is below.  It should be possible to do the 
> same for the "spiky" treble path, and perhaps get nicer methods. Can it be 
> done with more sensible calls than here?
>
> 720 Unnamed Surprise Minor (treble triple dodging)
>
> hl le   23456
> -------------
>        42635
> s  s    26435
> -  -    45623
> -------------
> 5-part
>
> hls=1; les=2; hl-=5; le-=4;
> method: &3-3-3-3.4-5-2-5-3-4-4-4-3, 1
>