[r-t] ringing related paper

[Philip Earis]

Prof. Holroyd:
"Here is a mathematics paper related to change ringing theory that people 
might be amused to see.  The main result can be interpreted as: any 
permutation may be achieved by a link method with a bounded number of 
changes of direction for each bell, regardless of the stage (specifically, 
10 changes of direction per bell is enough)..."

Interesting.  What is the maximum number of changes of direction a bell 
needs at stages 8, 10, 12?  What permutations at these stages require the 
maximum changes of direction?