[r-t] Pitman's 13440 change compositions
alan.reading at googlemail.com
Wed Aug 9 15:48:03 UTC 2017
Don - That is, while these compositions use all the tenors together lead
heads and ends, they are more profligate in their use of rows interior to
the various leads.
Yes I think that is exactly right. It's not to say that Philip's suggestion
of finding a set of 3 courses (presumably with the 7th in 3rds, 5ths, and
7ths relative to the tenor) that have all possible positions of
(1,7,8,parity) isn't achievable but I think it would be very much harder
because there isn't any wiggle room like in the tenors together examples.
On 9 August 2017 at 16:21, Don Morrison <dfm at ringing.org> wrote:
> [In response to various messages on how these compositions work.]
> I suppose a way to make it all work is to construct a bunch of courses and
> course fragments (the latter to fill in missing bits from the former, etc.)
> with the property that for any position of (1, 7, 8, parity), which in some
> cases might only occur in some of the courses or course fragments, whenever
> it does occur it is guaranteed to always appear as exactly the same row
> (for a given course head) for all the courses and course fragments in which
> it does occur. Note that this, combined with the implicit requirement that
> the courses and course fragments be true, implies such a four-tuple appears
> at most once in any one course or course fragment, which was the earlier
> conjecture of how this all works, I think.
> If this conjecture is true, I think it means such a scheme is going to be
> difficult or impossible to extend to use for a 40,320, since it depends
> upon throwing away some rows. That is, while these compositions use all the
> tenors together lead heads and ends, they are more profligate in their use
> of rows interior to the various leads.
> Does all this make any sense, or am I losing it?
> Don Morrison <dfm at ringing.org>
> "Inconceivable!" "You keep using that word!...I don't think it means
> what you think it does." -- William Goldman, _The Princess Bride_
> ringing-theory mailing list
> ringing-theory at bellringers.org
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