[r-t] Candidate definition #10a

[Don Morrison]

Here is a slightly revised version of Candidate Definition #10,
incorporating three of the improvements suggested.

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A block, B, is a sequence of rows. Every bell strikes exactly
once in each row. During the performance of B no bell strikes
except as part of exactly one of the rows of B. The number of
rows contained within B is its length. One or more bells may ring
in the same position in each and every row of B, and such bells
are non-changing bells. The stage, S, of B, is the number bells
ringing that are not non-changing bells.

Consider a block B of stage S. There are S factorial possible
different rows, which are together known as the extent at stage
S. B is true if every possible distinct row of the extent at
stage S occurs either N or N+1 times in B, for some N>=0. B is
complete if every row of the extent at stage S occurs exactly N
times, for some N>=1. B is incomplete if it is not complete.

A touch is a sequence of one or more blocks, all of stage >0,
rung in order, all on all of the same bells, with no bell
striking that is not a part of exactly one block. The length of
the touch is the sum of the lengths of its constituent blocks.

A touch is a peal if it has length >=5000, and all its
constituent blocks are true, and no more than one of its
constituent blocks is incomplete.

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-- 
Don Morrison <dfm at ringing.org>
"My first novel, _The Temple of Gold_, was published by Alfred A. Knopf.
(Which is now part of Random House, which is now part of R.C.A. which
is just part of what's wrong with publishing in America today, which is
not part of this story.)"        -- William Goldman, _The Princess Bride_