[r-t] Out of course treble-dodging minor

[Alexander Holroyd]

Awesome stuff!  I think it is a very short step from here to finding the 
minimum number of extents required to get all the methods.  (Although 
taking account of lead splicers and lead end variants would complicate 
things).

Ander

On Tue, 29 Dec 2015, John Danaher wrote:

> For the 147 methods the number's a bit larger. There end up being 1133
> maximal sets that admit an extent.
>
> Out of the 11 methods {Bg Bh Bp Bw Cc Cf Cn Dn Le Mp Pm}, any 5 form a
> maximal set, so that's 462 right there. That set of methods also shows up
> frequently in combination with others. For example, another 260 sets take 4
> of those 11 methods then add 1 of {C2 C3} and 1 of {Rc C1}, and another 162
> sets take 3 of those 11 methods and add one of {Bo Cz Li Qu Tr}.
>
> The full list is too long for an email, so I posted it to
> http://methodatlas.com/maximal-sets-147.txt . Extents achievable with only
> bobs are marked with a *, and the few that have only a single work above
> the treble are marked with a #.
>
> (All of the maximal same-above sets are also achievable with only bobs, but
> that's not the case for all sub-maximal sets: {Es Ox} and {Cf Es Ox} share
> work above the treble but can only achieve an extent with the aid of
> singles.)
>
> - John
>
> On Mon, Dec 14, 2015 at 3:45 AM Alexander Holroyd <holroyd at math.ubc.ca>
> wrote:
>
>> Here are the maximal sets of splicable methods from the standard 41
>> (ignoring lead-end variants and lead splicers).  As I said, a very short
>> list.  I would like to see the same thing for the 147.
>>
>> In course:
>>
>> Bm
>> Ke
>> Li
>> Wk
>> Bo Ne
>> Ak Nb Cl
>> Nb Sa Cu Cl
>> Ak Ch Sa Cu Cl
>> Nw Ak Ch Sa Cl
>> Bv Bo Du Cm Yo
>> Nw Sa Ch Cu Cl
>>
>> Out of course:
>>
>> Bm
>> Lf Ak Wm Nw
>> Ip Bo Cu Cm
>> Sa Bo Ws No
>> Bv We Cu Yo
>> Lo Ip Cu Cl
>> Lo Yo Cu Cl
>> Ip Cu Cm Lo
>> Ip Cu Cm Ne
>> Ip Cu Cm Yo
>> Ip We Cu Lo
>> Sa Ws Ne No
>> Lf Ak Wm Nb Ne
>> Lo We Du Yo Cu
>> We Yo Lo Bo Bv Du
>>
>> On Tue, 8 Dec 2015, Alexander Holroyd wrote:
>>
>>> That's awesome work John!
>>>
>>> Suggestion for what to look for: all _maximal_ sets of methods that
>> admit an
>>> extent.  It may take a bit of thought to figure out a good algorithm for
>>> this, but it should be doable, and the list will probably not be that
>> long.
>>> I did it for the surprise only by a pretty naive algorithm.  There were
>> only
>>> about 20 sets IIRC.
>>
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>