[r-t] MUG minor
pje24 at cantab.net
Sat Dec 5 12:41:36 UTC 2015
Matthew: "MUG minor, which was discussed in the very earliest days of the list and seems to be structurally similar to Erin, for which I don’t think a truly satisfactory answer was reached (I think all offered compositions still had half-lead calls, or multiple types of call).
Indeed, it would be good to revisit this. This is a more tractable problem for Mr Burlison and others to get stuck into.
To recap, MUG is a neat method with 8 changes per division (http://ringing.org/main/pages/method?title=MUG+Minor)
The challenge is to produce an extent (720 changes, ie 90 divisions) with just one type of call, only at the division end.
(I'm assuming nobody still has proved this isn't possible)
So the most naive exhaustive search is of size 2^90 (huge but vastly smaller than for Erin Triples) but this can easily be dramatically pruned.
As Mr Frye mentioned, the current "best solution" is a 5-part extent by Ander Holroyd, albeit this contains calls at both the division end and half-division (http://bellringers.net/pipermail/ringing-theory_bellringers.net/2004-September/006283.html)
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