[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
assumptions.
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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