[r-t] Minor principles with the extent in plain courses

Alexander Holroyd holroyd at math.ubc.ca
Tue Sep 28 03:00:09 UTC 2004

Below are the results of a computer search for new minor principles.  I
considered all possible principles with a symmetric lead, no single
changes, no 5ths, and no three blows in the same place, up to 24 changes
in the lead.  I have an algorithm which tries to determine whether there a
set of plain courses yielding the extent.  It doesn't guarantee to find
such a set if one exists, but it appears highly likely to in practice.
(I'll give a description of the algorithm at some point).

Interestingly, the search turned up almost nothing new - only things which
been produced before by human ingenuity / group theory, or simple
variations thereof.

2 ch/lead: Original (the course is a group)

8 ch/lead: Kidderminster (the course is a group)

12 ch/lead: Brussels Sprout, the same with 34 lead end, Hekaton, St Thomas
the Martyr (all use same group of order 120 for lead heads and lead ends)

20 ch/lead: Striking (the course is a group), variants with lead ends
16 (Pitman),34, their reverses,  and the following new variation:
&2.3-4.3-3.4.3-, le 34
bob=3, single=3456;  720: --s--s @ 6

24 ch/lead: Eureka (an extraordinary method...), its reverse

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