[R] getting all circular arrangements without accounting for order

Boris Steipe boris.steipe at utoronto.ca
Fri Mar 30 04:20:19 CEST 2018

If one is equal to the reverse of another, keep only one of the pair.


> On Mar 29, 2018, at 9:48 PM, Ranjan Maitra <maitra at email.com> wrote:
> 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
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