How to generate only rotationally-unique permutations?

[Arnaud Delobelle]

On 19 May 2012 06:23, John O'Hagan <research at johnohagan.com> wrote:
> To revisit a question which I'm sure none of you remember from when I posted it
> a year or so ago - there were no takers at the time - I'd like to try again with
> a more concise statement of the problem:
>
> How to generate only the distinct permutations of a sequence which are not
> rotationally equivalent to any others? More precisely, to generate only the most
> "left-packed" of each group of rotationally equivalent permutations, such that
> for each permutation p:

This makes me think of Lyndon words.  A Lyndon word is a word which is
the only lexicographical minimum of all its rotations.  There is a
very effective way of generating Lyndon words of length <= n.  It may
be possible to adapt it to what you want (obviously as Lyndon words
are aperiodic you'd have to generate Lyndon word of length d | n when
suitable).

-- 
Arnaud