# [r-t] Parity

Glenn Taylor gaataylor at blueyonder.co.uk
Tue Jun 19 19:43:20 UTC 2007

```5 bells:
The last row with 1 leading is: 15432
This requires 2 pairs to swap to get rounds
First row with 2 leading is 21345
Therefore 3 swaps to get from 15432 to 21345

6 bells:
ditto

7 bells:
3 swaps to get from 1765432 to 1234567 therefore 4 to get to 2134567

This demonstrates that although the first (n-1)! rows begin +1234..n then
the next set of (n-1)! rows begins with an even row for 5/6 bells but with
an odd row for 7/8. I came across this when writing a program that needed
each of the major course-heads to be mapped to its FCH. There *is* a pattern
but it gets reversed at predictable (?) intervals.

----
I was hoping to find a quick way to find the parity
based on finding an index of the row and analysing
that index. Since the parity doesn't behave nicely
that avenue seems prohibitive.
----

I didn't ever look at this, but filed away somewhere or other I do have a
means of applying a place notation to an index number in order to generate
the next index number (provided that the current index number is generated
from a set of "coefficients") if that's of any interest.

Glenn Taylor

```