[r-t] Notating jump changes

[Tim Barnes]

Further to my earlier post, the following is the CC Method team's proposal
for notating jump changes in the Methods Library.  We'd be pleased to
receive any feedback, either via this list or at methods at cccbr.org.uk.

As background, there was a discussion on this topic on this list in 2015,
including Don Morrison conducting a survey.  We used this as the starting
point for the Method team's discussions.  See:

https://lists.ringingworld.co.uk/pipermail/ringing-theory_bellringers.org/2015-May/thread.html

and also the first message in:

https://lists.ringingworld.co.uk/pipermail/ringing-theory_bellringers.org/2015-June/thread.html

Our notation proposal is in the draft next version of the Framework at:

https://tjbarnes23.github.io/method_ringing_framework/placenotation.html

In summary, we're proposing two different notations for jump changes that
are used depending on the type of jump change being notated.

The first notation, proposed by Ander Holroyd, comprises a pair of places
in round brackets, e.g. (xy).  This means: the bell in place x jumps to
place y, and all other bells in the place range x to y move one place in
the other direction to accommodate the jump.  So (14) applied to row 1234
results in 2341, and (31) applied to 213 results in 321.

Normal place notation rules apply outside the jump range, i.e. pairs of
bells cross, and leading and/or lying places are inferred if needed.  So
(14) applied to 123456 results in 234165, and (42) applied to 2143657
results in 2314567.

The second notation uses square brackets to specify how a set of contiguous
places are transposed to produce the next row.  So [5634] applied to
4321567 results in 3456217 (again, normal place notation rules apply
outside the jump range).

The two notations can be combined as needed, and/or combined with regular
places.  E.g. (24)5[876]9(T0) applied to 1234567890ET results in
134258769T0E.

A constraint that we specify is that the range of places in any bracketed
section of a change shouldn't overlap with any other places or place ranges
in the change.  E.g. (48)(7E)(06)(E5) isn't considered a validly-notated
change.

As an aside, Ander did prove, using a bipartite graph, in his June 2015 r-t
post that overlapping round-bracketed pairs do result in an
unambiguously-defined change (if the selected pairs of places are valid).
However, we thought this notation is more complex to interpret than its
square-bracketed equivalent.  E.g. (13)(24)(51) unambiguously defines a
change, but is probably less clear than using [53124].

Another problem with overlapping round-bracketed pairs is that it isn't
always readily apparent whether a change is valid.  E.g. (48)(7E)(06)(E5)
is a valid change, whereas (48)(7E)(96)(E5) is not.

However, non-overlapping round bracket notation is very efficient for large
single-bell jumps (e.g. (1T) in Jump Cyclic Maximus), and in fact, all
known jump methods rung to date (see my earlier post) can be notated just
with round brackets.

As above, the full description of our proposed jump change notation is on
the draft framework website.  Comments welcome.

Regards
Tim
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://bellringers.org/pipermail/ringing-theory/attachments/20191208/deeb6fae/attachment.html>