writing down minimum and maximum cyclical permutations

[Eugene McDonnell]

maximum odd
2 4 6 - - - -
- - - 7 5 3 1
2 4 6 7 5 3 1

maximum even
1 3 5 7 - - - -
- - - - 8 6 4 2
1 3 5 7 8 6 4 2

minimum odd
1 - 3 - 5 - 7
- 6 - 4 - 2 -
1 6 3 4 5 2 7

minimum even (this gets tricky)
write odd number pairs adding to n (say 10), first number smaller
1 9  3 7
write half n (5)
- -   - -  5
write even number pairs adding to n, first number larger
- -  - -  - 6 4   8 2
end with n
- -  - -  -  - -  - - 10
giving
1 9   3 7   5   6 4   8 2   10

Having written one of these, generate all the other max or min 
permutations by all rotations and all rotations of reversal, giving 2n 
altogether.

Eugene McDonnell