[r-t] FCH & Incidence
Robin Woolley
robin at robinw.org.uk
Sat Feb 10 09:00:29 UTC 2007
Recent correspondence about FCH groups reminds me of another curious
property, but this time to do with incidence.
It seems that if, say, we have the FCH 4625378 with incidence 8v7 ocurring,
as it does in Cambridge S8, then we can immediately write down:
a) FCH 4625378 (the inverse), incid. 7v8
and
b) FCH 6452738, incid. 8v4
and
c) FCH 5734268, incid. 4v8
as well as the other four members of the set. In this case, I use the
convention that the first place bell is in the plain course, the second in
the false course.
The first of these is well known and is capable of proof but I don't know
that the second tranformation is so well known.
In summary, if one FCH and its incidence is known, all other FCHs and
incidence from the treble in the same position can be written down
straightaway.
Further, this is so for Cambridge S8 but the falsenesses and incidences will
be identical for all other (LH) group b methods - if any group b method has
FCH 4625378 8v7, then the other incidences will be the same.
Further again, if one FCH has the pivot bell false against itself, then all
eight associated FCHs will have the pivot bell self-false. As an example of
this, see FCH 6274538 3v3 in Cambridge.
Finally, note I say 'seems' at the top of the post. My 'proofs' have not
been checked by anyone else, so it could all be nonsense. I did find it
strange that incidence is almost as easy to deal with as FCHs when I first
met it. It all comes down to clock arithmetic.
Best wishes
Robin.
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