[r-t] Pitman's 13440 change compositions

Don Morrison dfm at ringing.org
Wed Aug 9 15:21:13 UTC 2017

[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_
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