[R] getting all circular arrangements without accounting for order

[Ranjan Maitra]

Dear friends,

I would like to get all possible arrangements of n objects listed 1:n on a circle.

Now this is easy to do in R. Keep the last spot fixed at n and fill in the rest using permuations(n-1, n-1) from the gtools package.

However, what if clockwise or counterclockwise arrangements are the same? I know that half of the above (n - 1)! arrangements are redundant.

Is there an easy way to list these (n-1)!/2 arrangements? 

I thought of only listing the first half from a call to permuations(n - 1, n - 1), but while this holds for n = 4, it does not for n = 5. So, I am wondering if there is another function or tweak which would easily do this.

Many thanks in advance for any help. and best wishes,
Ranjan