Holroyd: Created page with 'Alexander Holroyd holroyd at math.ubc.ca Wed Sep 29 12:35:12 BST 2010 Here is an idea for an automated method for analysing the plans. For each pair of plans in the list (ie a …'

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Created page with 'Alexander Holroyd holroyd at math.ubc.ca Wed Sep 29 12:35:12 BST 2010 Here is an idea for an automated method for analysing the plans. For each pair of plans in the list (ie a …'

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Alexander Holroyd holroyd at math.ubc.ca
Wed Sep 29 12:35:12 BST 2010

Here is an idea for an automated method for analysing the plans.

For each pair of plans in the list (ie a few million pairs), do the
following. "Rotate" one of the pair through all 60 possible starting
rows. (Your plans are already in standard form, aren't they?) For each
such rotation, compare the two plans. Specifically, look to see whether
the two plans are identical except that one is obtained from the other by
replacing some set of leads all of method X with all method Y. If so, say
that there is a "simple splice" between the two plans. The simple splice
itself may be described by saying what methods X and Y are, and what the
set of leads is, in "standard form" (i.e. rotated to it's smallest version
in lexicographic order).

After this is done for all pairs, the set of simple splices that arise had
better be what exactly we expect, i.e. things like "2 copies of the
Cambride-Beverley 6-lead splice".

We now have a graph, whose vertices (nodes) are the plans, and whose edges
(links) are the simple splices. Break this graph up into its connected
components, or "clusters". Each cluster is a group of plans all of which
communicate with each other via simple splices.

For a start I would like to know how many clusters there are.

Now we want to analyse the clusters. Any cluster that contains a
single-method extent can be removed from the game, because these we
(hopefully) completely understand. For the others, it would be desirable
to nominate a "standard representative" plan from each cluster - the basic
plan which then gets embelished with various simple splices to form the
other members of the cluster. I'm not sure whether there is a canonical
way to do this in general, but one natural thing that springs to mind is
to list, for each cluster, the plans that have the smallest number of
methods, and see by hand which of these (if there is more than one) is the
most "natural".

Then one can summarize the whole thing by listing, for each cluster, its
standard representative, and the list of all simple splices it involves.
I suspect such a list would be quite manageable.

----

Richard Smith richard at ex-parrot.com
Wed Sep 29 19:57:24 BST 2010

There are 506 connected components of which 14 are simple.
The simple components contain the methods:

1. Sg
2. Nm So C3 C2 Pn
3. Nw Mo Ak Ct Mu Ch Av Ca Ke Ce Cd Sw Va Li Co Cc We Lo
Cu Cx Bn Pv Bt Le Md Mp C1 Cl Nb Wh Gl Fo Ml By Pm Ed
Kh Ww Lu Cz Cy Bh Os Bw Wf
4. Qu Sn Ti Sh Tr Km
5. Kt
6. Bl Wk
7. Fr Cg
8. Cj Nl
9. Du Yo Su He Bv Bk Cm Pr Ip Nf Bs Wa
10. Bu
11. Es Cv
12. Rc Bz
13. Bm Bc El Cr Wm St Lf Ro Sa Wo Te Ev Po Dt Ck Wt Di Ms
Do Dn Pe Wl Bg Kn Rs Ba Cs Fg Sk Ey Bp Wv Bo Hu Ki Lv
Cn Ri Dk Cf Ny Oc Ci Ks Ls Sd Ox No Ne Ab Ws Ad Ma Br
Ta Hm Ol Cb Ng Wi Cw Ns Sl Wr
14. Be Me

The full list of plans grouped into clusters is here:

http://ex-parrot.com/~richard/minor/147/plans-in-clusters.txt

Spliced treble-dodging minor - clusters - Revision history

Holroyd: Created page with 'Alexander Holroyd holroyd at math.ubc.ca Wed Sep 29 12:35:12 BST 2010 Here is an idea for an automated method for analysing the plans. For each pair of plans in the list (ie a …'