[r-t] Falseness in the plain course

Alexander Holroyd holroyd at math.ubc.ca
Fri Oct 21 19:41:56 UTC 2016

On Fri, 21 Oct 2016, pje24 at cantab.net wrote:

> My first question is: when does the first of these (false in the plain course)
> actually occur, ie when bolting a symmetric minor overwork onto a symmetric minor
> underwork?

In this particular setting it cannot occur under a few natural 

Consider a symmetric treble-dodging minor method in which every section is 
either of the form xPx or PxQ, where P and Q are place notation having 
exactly two places.  Suppose also that the half lead and lead end changes 
have two places made.  (But do not assume anything about the number of 
leads in the plain course, or regular lead ends).

Then any two rows within a section with the treble in the same place have 
opposite nature (aka parity).  On the other hand, the lead heads and lead 
ends of the plain course form an in-course group.  Therefore the plain 
course is true: if two rows were the same, they would have to occur in the 
same place in the half lead, but then the corresponding two lead 
heads/ends would be the same.

On the other hand, relaxing the rule about sections can give methods that 
are false in the plain course, e.g.:
&-34-4-2-3.2.34-3, l.e. 1

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