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

John Danaher jsd at alum.mit.edu
Tue Dec 29 04:08:07 UTC 2015

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

 - John

On Mon, Dec 14, 2015 at 3:45 AM Alexander Holroyd <holroyd at math.ubc.ca>

> 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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