[r-t] Red Square Hybrid Doubles
Alexander Holroyd
holroyd at math.ubc.ca
Wed Nov 12 02:02:26 UTC 2008
Here is the latest wacky doubles method:
125.145.3.123.1.345.125.1.345.123.1.3.125.145.3
120: pppsppps; single = 1 for last 145
http://www.campanophile.co.uk/show.aspx?Code=73986
It is one of very few rung methods with an odd number of changes in the
lead. The treble spends 3 blows in each place, giving a lead of length
15, and 4 working bells give a course of length 60. Two courses give the
extent.
It feels very different to ring from any of the usual things.
The 8 lead heads for the entire extent form the dihedral group D_8
(generated by 13245 and 14523). There are quite a few such methods
possible; unfortunately all have at least 3 blows in the same place.
Blue lines for all the ones with at most 3 blows, and at most 4 blows can
be found at:
http://www.math.ubc.ca/~holroyd/tp/tplines3.pdf
http://www.math.ubc.ca/~holroyd/tp/tplines4.pdf
(place notation is given as a string of one character per change - 0
denotes 123 and 6 denotes 345).
The Schreier graph for this group can be found at:
http://www.math.ubc.ca/~holroyd/schreier/graphs-ps/g13245-14523.ps
- for (slightly) more info see:
http://www.math.ubc.ca/~holroyd/schreier/
To get a method with these 8 rows as lead heads, you just need a tour
of this graph visiting each node exactly once (i.e. a Hamiltonian cycle).
cheers, Ander
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